CN103065525A - Manufacturing and using method of Goldbach conjecture proving Great Wall diagram template - Google Patents

Manufacturing and using method of Goldbach conjecture proving Great Wall diagram template Download PDF

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CN103065525A
CN103065525A CN2013100336944A CN201310033694A CN103065525A CN 103065525 A CN103065525 A CN 103065525A CN 2013100336944 A CN2013100336944 A CN 2013100336944A CN 201310033694 A CN201310033694 A CN 201310033694A CN 103065525 A CN103065525 A CN 103065525A
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odd number
goldbach
great wall
conjecture
prime
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CN103065525B (en
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李中平
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Abstract

The invention relates to a manufacturing and using method of a Goldbach conjecture proving Great Wall diagram template, relating to the technical field of science and education. The manufacturing and using method of the Goldbach conjecture proving Great Wall diagram template aim at solving the technical problems that the Goldbach conjecture is difficult to visually and effectively demonstrate in the existing mathematical education, and the like. The Goldbach conjecture proving Great Wall diagram template comprises a Goldbach conjecture proving Great Wall diagram template cover plate (1), a template bottom plate (2), a plurality of even rulers (3), a plurality of odd prime rulers (4), a plurality of odd difference shift rulers (5), a Great Wall line (6), a median line (7), a ladder line (8), a Goldbach conjecture 1+1 elliptical drawing board (9), a Chen Jingrun theorem 1+2 elliptical drawing board (10) and two Goldbach problem Everest drawing boards (11).

Description

The Goldbach's Conjecture proves Great Wall figure template making and using method
Technical field
The present invention relates to the Science and education technical field, particularly a kind of Goldbach's Conjecture who is applied to the teaching instruction Goldbach's Conjecture of middle and primary schools proves Great Wall figure template making and using method.
Background technology
The immediate existing mechanism of the present invention and device are that the declarer has obtained invention utility model patent certificate " planar demonstrator for Goldbach conjecture " afterwards new product and new technology and the method for creativity and innovation." planar demonstrator for Goldbach conjecture " this patent and technology, can only be confined to allow the reader understand international mathematics difficult problem Goldbach's Conjecture in from 6 to 100 the positive even numbers scope, use " planar demonstrator for Goldbach conjecture ", can not represent to prove Goldbach's Conjecture's reliable method, in presentation process, not show this natural law under covering in demonstration device of Goldbach's Conjecture.Simultaneously, in " planar demonstrator for Goldbach conjecture ", the 1st row from top to bottom, the odd prime position of arranging is from small to large fixed, the reader be not easy to according to each even number M in 6 to 100 scopes deduct column odd number prime number Y gained poor N whether be expert at corresponding to the odd number prime number X of the 1st row with delegation, thereby reduced the demonstration effect, weakened the effect that student and reader use " Goldbach is guessed planar demonstrator " study.
Summary of the invention
The present invention is intended to solve and is difficult to carry out for the Goldbach's Conjecture technical matters such as effectively demonstration directly perceived in the existing mathematical education, has convenient operation to provide, good demonstration effect, the Goldbach's Conjecture that is suitable for teachers in primary and middle schools and the research Goldbach's Conjecture's of Mathematics Discipline scientific research institutions of colleges and universities the advantages such as proof prove Great Wall figure template making and using method.
The objective of the invention is to be achieved through the following technical solutions.
Goldbach's Conjecture of the present invention proves Great Wall figure template making, prove Great Wall figure template cover plate 1, template plate 2 by the Goldbach's Conjecture, even number chi 3, odd number prime number chi 4, odd number move 5 some of poor chis, Great Wall line 6, neutrality line 7, high ladder line 8, the oval drawing board 9 of Goldbach's Conjecture 1+1, the oval drawing board 10 of Chen Jing profit theorem 1+2, two formations such as Mount Everest drawing board 11 of Goldbach problem.
Described Goldbach's Conjecture refers to can be write as two odd number prime number X and Y's and X+Y greater than 4 even number M;
Described prime number refer to if positive integer except 1 and he itself, do not have other approximate number, this positive integer is prime number so, minimum prime number is 2, is unique even number prime number, all the other all prime numbers all are odd numbers, are the odd number prime numbers greater than 2 prime number namely;
Described template cover plate lower surface and template plate upper surface are printed on title and the little square net that the Goldbach's Conjecture proves Great Wall figure, relatively reverse, overlook in the same way, specification is identical, cover plate lower surface reverse printed, the different metal wire of three kinds of colors or the line of other environment-friendly materials are imbedded in plate upper surface forward printing, template cover plate also grooving, are used for respectively representing Great Wall of the present invention line, high ladder line and neutrality line.On template plate, all dug the groove that the degree of depth, width and length are arranged in every delegation form, be to insert the groove that odd number moves poor chi or even number chi;
Described even number chi upper surface has printed 4,6,8,10,12 ... a row positive even numbers, can in base plate, move in the grooving of the 1st row institute the 2nd row the position;
Described odd number prime number chi upper surface has printed 3,5,7,11,13,17,19,23, a row odd number prime number, described odd number moves poor chi and asks numeral on the prime number chi and graphic making out according to what fork went that the prime number method of multiplicity makes, uses odd number and moves data above the poor chi, remove by fork go close the number and 1, made odd number prime number chi;
Four jiaos of described template plate and template cover plates have the hole of 1 circle, are convenient to be screwed the position of cover plate and base plate, the form that is printed on cover plate and the base plate is overlapped, " Goldbach's Conjecture proves Great Wall figure " pattern plate bolster is made in assembling, is called for short Great Wall figure template
As shown in Figure 1,3 metal wires that color is different are inserted in Great Wall figure template upper surface grooving, show respectively Great Wall line, high ladder line and neutrality line.In pattern plate bolster, in the 1st groove, insert the even number chi, in other grooves, insert respectively 1 odd number and move the phenomenon that misplaces after poor chi translation does not occur, consist of " Goldbach's Conjecture proves Great Wall figure " template virgin state.The application odd number moves poor chi and moves method, and from the 2nd row, the parallel odd number moves poor chi successively, obtains showing the template of " Goldbach's Conjecture proves Great Wall figure ".Described Goldbach's Conjecture proves Great Wall figure, by proving that the Goldbach's Conjecture translation odd number moves the result who obtains behind the poor chi in the figure template of Great Wall, shows redly, the chromatic pattern of black and the color such as blue.In this figure, also printed the Great Wall line of Goldbach's Conjecture's proof, the corresponding curve map that forms 3 kinds of different colours of neutrality line of the high ladder line of Goldbach's Conjecture's proof and Goldbach's Conjecture's proof.
Described Goldbach's Conjecture Great Wall line method for making, such as Fig. 8 and shown in Figure 14, in " Goldbach's Conjecture proves Great Wall figure ", from positive even numbers 6, from left to right ascending, see from top to bottom in each even number column, draw the line segment of a purple on one side of the lower square of the odd number prime number of the 1st redness of not gone by fork, keep straight on up or down again, the line segment of a purple is drawn on the limit of the lower square of the odd number prime number of the 1st redness of then not gone by fork second positive even numbers column, carry out successively, draw the Goldbach's Conjecture and prove the Great Wall line.
Make the concrete grammar of Great Wall line, below positive even numbers 6 columns, a unique odd number prime number 3 in the 2nd row is only arranged, the line segment of just drawing a purple below 3 indicates; Below positive even numbers 8 columns, there are odd number prime number 5, the 3 row that odd number prime number 3 is arranged at the 2nd row, just below the 1st odd number prime number 5 below the positive even numbers 8, draw the line segment of a purple; Below positive even numbers 10 columns, the 1st odd number prime number is 7, just draws the line segment of a purple below the 1st odd number prime number 7; Below positive even numbers 12, the 1st odd number prime number is 7, just draws the line segment of a purple below odd number prime number 7; Carry out successively.Then from the purple line segment of the odd number prime number 3 of positive even numbers 6 columns, with purple line segment longitudinally, the line segment of the purple that each row has drawn after connecting successively up or down or to the right, obtaining at last below the 1st row positive even numbers forming a broken line with the very similar purple of the Great Wall, is exactly the Great Wall line of Goldbach's Conjecture proof of the present invention.
The high ladder line method for making of described Goldbach's Conjecture's proof, such as Fig. 9 and shown in Figure 14, in " Goldbach's Conjecture proves Great Wall figure ", the position is as the main reference object after moving poor chi translation take each row odd number, the standard of the odd number prime number 3 of the minimum of positive even numbers M column below as object of reference, namely from positive even numbers 6 is expert at, from small to large from left to right, the line segment of the blueness of picture of turning right below odd number prime number 3 indicates, to the left side of existing odd number prime number 3 columns of listing of back, end, if institute's setting-out meets by what fork went and closes number, just closing several columns at this sees from the bottom up, find the 1st odd number prime number, the line segment of drawing 1 blueness below this odd number prime number indicates, connect successively from left to right up or down at last the line segment of the drawn blueness in odd number prime number below with vertically blue line segment backward, form at last the high ladder line that a Goldbach's Conjecture of the present invention proves.
The method for making of described Goldbach's Conjecture's neutrality line such as Figure 10 and shown in Figure 14, in " Goldbach's Conjecture proves Great Wall figure ", is directly determined by the even number M greater than 4 in the 1st row, if
Figure BDA00002790390800031
Be the odd number prime number, just in the middle of this odd number prime number place square of M column, draw a flavous line segment that crosses this odd number prime number, if
Figure BDA00002790390800032
Not the odd number prime number, just in positive even numbers M column, with
Figure BDA00002790390800033
Be references object, for all greater than
Figure BDA00002790390800034
Odd number, see from the bottom up, find the 1st odd number prime number, again with
Figure BDA00002790390800035
Be references object, to all less than
Figure BDA00002790390800036
Odd number, see from top to bottom, find the 1st odd number prime number, on the centre position between these two odd number prime numbers, draw a flavous line segment that crosses this positive even numbers column, connect successively from left to right up or down drawn flavous line segment with golden yellow line segment longitudinally at last backward, draw a neutrality line of Goldbach's Conjecture's proof.
Making the concrete grammar of neutrality line, is in " Goldbach's Conjecture proves Great Wall figure ", for positive even numbers 6, because half of 6 is odd number prime number 3, just laterally draws a golden yellow line segment that crosses 6 columns in square grid centre position, 3 places and indicates; For positive even numbers 8, because half of 8 is 4, and 4 be not the odd number prime number, and take 4 as object of reference, see from the bottom up, 1st the odd number prime number larger than 4 is 5, take 4 as object of reference, see from top to bottom, be 3 than 4 the 1st little odd number prime numbers, afterwards, just laterally drawing a golden yellow line segment that crosses positive even numbers 8 columns in the centre position of odd number prime number 5 and odd number prime number 3 indicates; For positive even numbers 10, because half of 10 is 5, and 5 are odd number prime numbers, just draw a golden yellow line segment that crosses positive even numbers 10 columns in 5 places square intermediate lateral and indicate; For positive even numbers 12, because half of 12 is 6, and 6 be not the odd number prime number, take 6 as object of reference, sees from the bottom up, the 1st odd number prime number greater than 6 is 7, take 6 as object of reference, see that from top to bottom the 1st odd number prime number less than 6 is 5, and 5+7=12 indicates so laterally draw a golden yellow line segment that crosses positive even numbers 12 columns in 7 and 5 centre position; For positive even numbers 14, because half of 14 is 7, and 7 are odd number prime numbers, just draw a golden yellow line segment that crosses 14 columns in square grid centre position, 7 places and indicate; For positive even numbers 16, because half of 16 is 8, and 8 be not the odd number prime number, so 8 be object of reference, sees from the bottom up, the 1st odd number prime number greater than 8 is 13, and take 8 as object of reference, see that from top to bottom the 1st odd number prime number less than 8 is 3, and 13+3=16 just laterally draws a golden yellow line segment that crosses positive even numbers 16 columns in 13 and 3 centre position; Carry out like this, from positive even numbers 6 is expert at, vertically backward downward with golden yellow line segment afterwards, or upwards connect successively from left to right the golden yellow line segment of each bar that has drawn backward, form at last the neutrality line of Goldbach's Conjecture's proof.
For the convenience of using, guarantee to make the Goldbach's Conjecture and prove that Great Wall figure template do not make mistakes, each odd number prime number of the figure grid left side, Great Wall first row is moved to Goldbach's Conjecture's high ladder line left side, connect with a plus sige "+", plus sige "+" is adjacent with the positive odd number 1 that odd number moves on the poor chi, the meaning is as the 1st addend X among the X+Y=M this odd number prime number X of every row, Goldbach's Conjecture's high ladder line the right with each the odd number prime number in the delegation as the 2nd addend Y, form proof Goldbach's Conjecture's 1+1 type addition formula, simultaneously, all marked the line segment of a band arrow " → " in Great Wall figure the 2nd row or the 3rd row, expression moves to the left side of high ladder line on the right of the arrow " → " with arrow " → " left side the 1st row of being expert at the odd number prime number of delegation.
The oval drawing board synoptic diagram of described Goldbach's Conjecture 1+1, as shown in figure 11, be to make with a bluish oval cardboard, be printed on the literal of 4 row purples in upper surface inside, the first row is " Goldbach's Conjecture 1+1 ", the 2nd row is " 6=3+3; 8=3+5,10=3+7 ", and the 3rd row is " 12=5+7; 14=3+11 ", and the 4th row is suspension points " ... ".The lower left that the oval cardboard of the band colour that is printed on 4 style of writing words of making is sticked in the figure form of Great Wall forms.Also can adopt transparent organic glass or other environment-friendly materials to do.
The oval drawing board synoptic diagram of described Chen Jing profit theorem 1+2, as shown in figure 12, to make with orange oval cardboard with 1, be printed on the literal of 4 row black in upper surface inside, the 1st row is " Chen Jing profit theorem 1+2 ", and the 2nd row is " 12=3+3 * 3; 14=5+3 * 3 ", the 3rd row is " 16=7+3 * 3,18=3+3 * 5 ", and the 4th row is suspension points " ... ".The lower left that the oval cardboard of the band colour that is printed on 4 style of writing words of making is sticked in the figure form of Great Wall forms.Also can adopt transparent organic glass or other environment-friendly materials to do.
Two oval cardboards making with Goldbach's Conjecture 1+1 synoptic diagram and Chen Jing profit theorem 1+2 synoptic diagram can longitudinal arrangement, also can be transversely arranged, decide on the line number of Great Wall figure grid.
Two Mount Everest drawing boards of described Goldbach problem as shown in figure 13, are the drawing boards that is printed on the transparent poly (methyl methacrylate) plate of a rectangular shape.Near two separate mountain peaks of rising sheer from level ground on the level ground are arranged on this drawing board, and the large theorem of Goethe Bach that expression is relevant with Goldbach's Conjecture 1+1 is the addition of K odd number prime number, form a series of propositions of the form of " 1+1+1+ ...+1+1 ", that mountain peak slightly high with the left side on Figure 13 represents that 1+1+1+ is arranged ... + 1+1,1+1+1+1+1,1+1+1+1,1+1+1,1+1, when K=2, the 1+1 that assigns a topic exactly, the present invention says into Goldbach's Conjecture 1+1.The relevant large theorem 1+K of Chen Jingrun of another expression and Chen Jing profit theorem 1+2 adds a series of propositions of 1 odd number prime number after wherein K and 1 represents respectively to be multiplied each other by K odd number prime number, formation " 5+3 * 3 * 3 * ... * 3 * 3 " form, represent have with that lower slightly mountain peak of the upper the right of figure ..., 1+5,1+4,1+3,1+2 is in proposition 1+K, when K=2, the 1+2 that assigns a topic exactly is the result of Chen Jing profit proof, and the present invention says into " Chen Jing profit theorem 1+2 ".
Two Mount Everest drawing boards of Goldbach problem stick on the suitable position, the right of " Goldbach's Conjecture proves Great Wall figure template ".In the mid-lower lower left of Fig. 1, be convenient to describe.
The having of described Goldbach's Conjecture separate all positive even numbers in the interval can be write as two odd number prime numbers and; Described Goldbach's Conjecture without separate all positive even numbers in the interval all can not be write as two odd number prime numbers and.
Among the described Great Wall figure odd number prime number X corresponding to odd number prime number Y and the left side that Y is expert at the 1st row on the solution curve arranged equal positive even numbers M in the odd number prime number Y column the first row with X+Y.
Described order of magnitude Great Wall in turn translation method of figure template and both sides folder translation method always can be used having in the less scope and separate interval interval without separating in the larger scope of covering, so that Goldbach is thought of as is vertical.
The order of magnitude template of described Great Wall figure such as Figure 15, Figure 16 and shown in Figure 17, refers to the closed interval [6,2 " Goldbach's Conjecture proves Great Wall figure " m] on, if greater than 2 mMinimum odd number prime number be X 1, and closed interval [6, X 1+ 3] be that the interval of solution, so closed interval [6, X are arranged 1+ 3] sub-range [6,2 m] must be that the interval of solution is arranged, just say by closed interval [6, X 1+ 3] it is 2 that the part Great Wall figure that determines is called the order of magnitude mGreat Wall figure template.
Of the present invention have separate interval and without separating interval concept, refer on " Goldbach's Conjecture proves Great Wall figure " template, in the interval of being determined greater than two even numbers of 4 by the 1st row, if all even numbers can be write as two odd number prime numbers and, such interval is called the interval of solution, if all even numbers all can not be write as two even numbers and, such interval is called without separating interval.
On " Goldbach's Conjecture proves Great Wall figure " template, positive odd number 1 lucky positive even numbers 4, the 1 row and the 2nd row over against the 1st row that the odd number of the 2nd row moves on the poor chi is corresponding, can find out, as long as in below the 2nd row of the positive even numbers M column of the 1st row odd number prime number Y is arranged, M-Y=3 is so necessarily arranged, i.e. M=3+Y, like this, twin prime numbers 5 and 7,11 and 13,17 and 19,29 and 31 by the 2nd row, Deng the closed interval [6,10] of determining in the 1st row, [14,16], [20,22], [32,34], on all positive even numbers, can be write as two odd number prime numbers and, all these intervals all be have separate interval, closed interval [28,30], [36,38], [52,54], [58,60], [58,60], [66,68], [78,80], [88,90], [94,98] ... and open interval (10,14), (16,20), (22,26) ... all positive even numbers of determining, all in the 2nd row, all can not be write as two odd number prime numbers and, all such intervals all are interval without separating.
Described " Goldbach's Conjecture proves Great Wall figure " has solution curve, as shown in figure 18, refer in " Goldbach's Conjecture proves Great Wall figure ", from the i row, towards the lower right i row and (i+1) row are pitched two odd number prime numbers that the odd number that goes closes several belows and couple together with a smooth curve, such curve is called " Goldbach's Conjecture proves Great Wall figure " solution curve.
" Goldbach's Conjecture proves Great Wall figure " has solution curve is the natural law of " Goldbach's Conjecture proves Great Wall figure ", and the odd number prime number that is not gone by fork in being listed as is formed naturally by each, as shown in figure 18.
Use the Goldbach's Conjecture to prove Great Wall figure template, can directly find out the certain conclusion of setting up of Goldbach's Conjecture.
Make the Goldbach's Conjecture and prove principle and the method for Great Wall figure template, from positive even numbers 6, can be ad infinitum positive even numbers M be had to make the solution that the Goldbach's Conjecture sets up and naturally extend to endless scope.
Use the present invention's fork to remove the prime number method of multiplicity, can obtain natural number sequence 1,2,3,4,5,6,7,8,9 ... all odd number prime numbers, remove even number, in endless range, make desirable odd number and move poor chi (contain fork go close number) and odd number prime number chi (do not contain and pitch the number that closes that goes).
Described fork removes the prime number method of multiplicity, is that the present invention invents the method for obtaining all odd number prime numbers in natural number sequence, can be in the lower crowd of middle and primary schools and various circles of society's educational level prevalence and popularize the method that everybody can both be learned.
1, fork goes the prime number method of multiplicity that following step is arranged.
The 1st step in the plane from small to large, was arranged in order positive integer from left to right, and 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24 ...
In the 2nd step, fork removes minimum positive odd number 1, because positive odd number 1 is not neither prime number is again to close number.
In the 3rd step, judge that 2 is minimum prime numbers, because 2=1 * 2, namely 2 only have 1 and 2 two approximate number, according to the definition of prime number, except 1 and itself, there is not other approximate number, such positive integer is prime number ", can judge that 2 is prime numbers, because in positive integer; minimum positive integer 1; and 1 neither prime number is not again to close number, so 2 is minimum prime numbers.
In the 4th step, on the right of prime number 2, it is numbers of the multiple of prime number 2 that fork goes all, and just fork has gone 4,6,8,10,12,14,16,18,20,22,24 ..., in all positive integers that the right 2 is not gone by fork, finding the 1st positive odd number that is not gone by fork is 3.
The 5th step, judge that 3 is prime numbers because 1,2, in 3,3=1 * 3, two approximate numbers 1 except 3 and 3 itself, also have in addition a positive integer 2 so that 3 ÷ 2=1.5, namely 2 is aliquant 3, so 3 is prime numbers.
In the 6th step, on the right of prime number 3, it is numbers of the multiple of prime number 3 that fork goes all, and just fork has gone 6,9,12,15,18,21,24 ..., in all positive integers that the right 3 is not gone by fork, finding the 1st positive odd number that is not gone by fork is 5.
The 7th step, judge that 5 is prime numbers, the number that removes all multiples of 5 is pitched on the right 5, and just fork has gone 10,15,20,25 ..., in all positive integers that fork does not go of the right 5, finding the 1st positive odd number that does not have fork to go is 7.Judge that 7 is prime numbers.
.......................
Go on successively, just can obtain all prime numbers that are distributed in the natural number sequence.Simple and clear is illustrated as follows:
Figure BDA00002790390800071
Positive integer is in line, has finished above-mentioned work, just made " fork goes the prime number method of multiplicity to ask the prime number chi ", as shown in Figure 5.
2, make the method that odd number moves poor chi
As shown in Figure 5, use " fork goes the prime number method of multiplicity to ask the prime number chi ", or gone plain method of multiplicity to ask the ordered series of numbers of prime number by fork.
Figure BDA00002790390800072
In, remove all by the fork number of uncoupling, namely remove
Figure BDA00002790390800073
Also will remove the even prime number 2 that does not have fork to go, pitch the odd number prime number that goes and the odd number prime number mixing of not gone by fork by remaining quilt, horizontally-arranged becomes delegation from left to right from small to large, is printed on the transparent organic glass, makes odd number and moves poor chi, as shown in Figure 6.Also can be made into iron sheet chi, the plank chi of cuboid, also can make paper using, iron sheet, copper sheet, cloth etc. make the tape measure shape, move the right-hand suspension points of poor chi " ... " the right at each odd number and be drilled with 1 aperture, wear 1 line, be convenient to stretch in use parallel.
3, make the method for odd number prime number chi
Go the prime number method of multiplicity to ask the ordered series of numbers of prime number by fork
Figure BDA00002790390800081
In, except even prime number 2, all odd number prime numbers that is not gone by fork, perpendicular forming a line from top to bottom is printed on the transparent organic glass from small to large, makes odd number prime number chi, as shown in Figure 7.Only print 1 odd number prime number in each square grid, and above 3, stay the square grid of a blank, the opposing party's suspension points " ... " aperture of lower drill with ferrule is worn 1 printed line, is convenient to mobile.
Use odd number prime number chi, prove in the figure pattern plate bolster of Great Wall the Goldbach's Conjecture and move, can read rapidly or write the needed addition formula of Goldbach's Conjecture of issuing a certificate.
4, even number chi method for making
As shown in Figure 4, positive even numbers since 4, by arraying from left to right into from small to large 1 row, is printed on the transparent organic glass, make scope for " 4,6,8,10; ..., 100 ", " 102,104,106; ..., 198,200 ", " 202,204,206; ..., 298,300 " different even number chis.When using, can use continuously two or numerous even number chi, enlarge the scope that the Goldbach's Conjecture proves that Great Wall figure uses, more convenient than using planar demonstrator for Goldbach conjecture.
5, odd number prime number chi using method
In " Goldbach's Conjecture proves Great Wall figure ", requirement according to the proof Goldbach's Conjecture, positive even numbers M is write as the form of X+Y, if positive even numbers M column is positioned at the Goldbach's Conjecture proves figure template centre position, Great Wall or take over, be not easy to the to the left odd number prime number of Great Wall figure the 1st row of reader, perhaps because the too many sight line of numeral is disorderly obscured with mesh lines, just use odd number prime number chi.Grid on the 1st row at the square blank grid of 3 tops on the odd number prime number chi and positive even numbers M-2 place is overlapped, in the M column, see from top to bottom, each odd number prime number can be used as Y, a left side is seen on the odd number prime number chi with Y at the odd number prime number X with delegation, just can be write as the form of M=X+Y, one is used for proving the effective addition formula of Goldbach's Conjecture exactly, or the result who directly reads X+Y=M.
For example, use " Goldbach's Conjecture proves Great Wall figure ", require the solution of Goldbach's Conjecture's proof of 68, just odd number prime number chi is lain in positive even numbers 66 columns, make square blank grid on the odd number prime number chi cover the square grid of positive even numbers 66, see from top to bottom, positive even numbers 68 columns one have 61,37,31,7 totally 4 numbers, on odd number prime number chi, corresponding 4 odd number prime numbers 7,31,37,61, at this moment, can see 61 in even number 66 columns immediately, read 68=7+61, seeing 37, read 68=31+37, seeing 31, read 68=37+31, regard 7 as, read 68=61+7.
Goldbach's Conjecture of the present invention proves that Great Wall figure template is made and the beneficial effect of using method: make the Goldbach's Conjecture and prove Great Wall figure template, can the Facing the whole group middle and elementary school student and the student of the kindergarten top class in a kindergarten, particularly popularize the epoch of reducing at the vast students ' practical ability in China town and country, carry out the student's activities of popularizing the Goldbach's Conjecture, introduce after the Goldbach's Conjecture, guiding student utilizes patent of the present invention and waste and scrap, mutually cooperation, produce jointly out the Goldbach's Conjecture and prove Great Wall figure template, then use Template Learning addition and the subtraction of making, existing keen interest, good effect is arranged again, even do the scope of template littlely, for example just do in 100, or in 1000, can write out various conclusions that can in limited positive integer scope, prove the certain establishment of Goldbach's Conjecture.
Prove Great Wall figure template producing principle and result of use according to the Goldbach's Conjecture in any range, overcome the shortcoming of planar demonstrator for Goldbach conjecture, increase function, can directly find out Goldbach's Conjecture's certain conclusion of setting up in infinite range from 3 different angles.
Make the Goldbach's Conjecture and prove Great Wall figure, simplify the structure, be easy to make, failure rate is low is not easy to make mistakes, and is safe and reliable, energy-conserving and environment-protective, be convenient to reader's operation, be conducive to answer prior art and Great Wall figure template, utilize " Goldbach's Conjecture proves Great Wall figure " of existing four-color press printing color." Goldbach's Conjecture proves Great Wall figure " about a large amount of publication and printing 1000mm * 400mm is involved in pen container or the school bag of packing into, enters in the student's desk, uses for the students self study plus-minus method, or joins Enlightening abacus, learns signed magnitude arithmetic(al) and uses the abacus rechoning by the abacus.
Utilize prior art, can produce teaching aid and wall chart " Goldbach's Conjecture proves Great Wall figure template " and " Goldbach's Conjecture proves Great Wall figure " for the middle and primary schools laboratory in batches.
The present invention is by Shenzhen printing enterprise trial-production " Goldbach's Conjecture proves Great Wall figure " painted scroll, also utilize the immaterial world cultural heritage technical design of the sharp Hunan embroidery in sky, Changsha to make " the Hunan embroidery Goldbach's Conjecture proves Great Wall figure ", make the collection elaboration that can enter the National Museum such as The National Museum of China or the U.S., Britain, Germany, can match in excellence or beauty with " Riverside Scene at the Pure Moon Festival " and " chanting Fuchun Village figure ".
Description of drawings
Fig. 1 is that the present invention's Goldbach's Conjecture proves Great Wall figure template synoptic diagram one
Fig. 2 is the present invention's template cover plate grid chart synoptic diagram
Fig. 3 is the present invention's template plate grid chart synoptic diagram
Fig. 4 is the present invention's even number chi synoptic diagram
Fig. 5 is that the present invention's fork goes the prime number method of multiplicity to ask prime number chi partial schematic diagram
Fig. 6 is that the present invention's odd number moves poor chi partial schematic diagram
Fig. 7 is the present invention's odd number prime number chi partial schematic diagram
Fig. 8 is the Great Wall line partial schematic diagram on the present invention's the template cover plate
Fig. 9 is the high ladder line partial schematic diagram on the present invention's the template cover plate
Figure 10 is the neutrality line partial schematic diagram on the present invention's the template cover plate
Figure 11 is the oval drawing board synoptic diagram of the present invention's Goldbach's Conjecture 1+1
Figure 12 is the present invention's the oval drawing board synoptic diagram of Chen Jing profit theorem 1+2
Figure 13 is two Mount Everest drawing boards of Goldbach problem synoptic diagram of the present invention
Figure 14 is that the present invention's Goldbach's Conjecture proves Great Wall figure partial schematic diagram
Figure 15 is that the present invention's the order of magnitude is 2 5Great Wall figure template synoptic diagram
Figure 16 is that the present invention's the order of magnitude is 2 6Great Wall figure template synoptic diagram
Figure 17 is that the present invention's the order of magnitude is 2 7Great Wall figure template partial schematic diagram
Figure 18 is that the present invention's it " Goldbach's Conjecture proves Great Wall figure " has the solution curve synoptic diagram
Figure 19 is it " odd number table of primes " synoptic diagram of the present invention
Figure 20 is the present invention's translation number magnitude Great Wall figure template synoptic diagram
Figure 21 is that the present invention's translation odd number moves the vertical covering of poor chi with civilian sketch
Figure 22 is for proving Great Wall figure template synoptic diagram two for the present invention's Goldbach's Conjecture
Embodiment
Detailed construction of the present invention, application principle, effect and effect with reference to accompanying drawing 1-22, are explained by following embodiment.
Fig. 1 is Great Wall of the present invention figure template synoptic diagram one, Great Wall figure template is erect in the diagram forward and is placed, the front is template cover plate and synoptic diagram thereof, the back is template plate, left side and top are printed with the Chinese character of redness " Goldbach's Conjecture proves Great Wall figure ", indicate 1 to 11 sequence number among the figure, wherein 1 is the template cover plate, the 2nd, template plate, the 3rd, even number chi, the 4th, odd number prime number chi, the 5th, odd number moves poor chi, the 6th, the Great Wall line, the 7th, neutrality line, the 8th, the high ladder line, the 9th, the oval drawing board of Goldbach's Conjecture 1+1, the oval drawing board of the 10th, Chen Jing profit theorem 1+2, the 11st, two Mount Everest drawing boards of Goldbach problem etc.
Fig. 2 is the grid synoptic diagram that is printed on Great Wall figure template cover plate lower surface.Grid among the figure is the identical square net of the length of side, respectively draw a line segment in the 1st grid in the upper left corner to the right with to the top from the lower right corner, this little square is divided into 3 parts, from the bottom to top, write out respectively in the clockwise direction " X ", " Y ", the Latin alphabet of " M " three capitalization, wherein " X " of capitalization expression grid left side first row the 2nd walks to the odd number prime number 3,5 of printing in capable each grid of N, 7,11,13,17,19,, except the 1st row of " Y " of capitalization expression grid left side and except the 1st row of grid top, odd number moves the odd number prime number that poor chi moves to behind the assigned position not the redness of being gone by fork in grid, the positive even numbers 4 of prining and brushing to N from the 2nd row in " M " expression grid top the 1st row of capitalizing, 6,8,10,12 ...
Fig. 3 is the grid synoptic diagram that is printed on Great Wall figure template plate upper surface.The size of grid is identical with the template cover plate with specification among the figure.In the grid chart of template plate, it is capable to walk to n from the 2nd from top to bottom, has all dug a groove, form the groove of rectangular shape, dig to the boundary line of the 2nd row and the 1st row, odd number moves poor chi and just can move around in this groove, in the groove of the 1st row excavation, can insert the delegation's even number 4,6,8 that is printed with since 4,10,12,14, the even number chi, its specification is identical with the specification of the transversely arranged delegation's even number of template cover plate lower surface reverse printed, the 1st row odd number prime number 3 of brush since 3 of prining, 5,7,11,13,17,19,23,29,, its specification is identical with the specification of the vertically disposed 1 row odd number prime number of printing on the odd number prime number chi.
Fig. 4 is even number chi partial schematic diagram of the present invention.On the even number chi, from left to right delegation's positive even numbers of printing is 4,6 from small to large, 8,10,12,14,16,18,, 96,98,100 ..., printed in last little square one have 3 suspension points " ... " suspension points " ... " the right be drilled with a circular aperture, the cover single line, be convenient to the pulling.The length of even number chi is not limit, and it is identical also can to print several specifications, but the different even number chi of numeral, during use, then demonstration, for example, 1 even number of the 1st chi most end is that the 1st even number that 100, the 2 chis begin is 102, and last 1 even number is 200, be printed on respectively on each even number chi " 102,104; 106,108 ..., 158,160; 162 ..., 196,198,200 " and " 202; 204,206,208 ..., 254,256 ..., 296,298,300 " etc.
Fig. 5 is that fork of the present invention props up the prime number method of multiplicity and asks prime number chi partial schematic diagram, and fork goes the prime number method of multiplicity to ask the chi of prime number or ask and close several chis, is rectangular parallelepiped plate shape, and upper surface has printed natural number sequence 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24 ...During making, at first fork removes positive odd number 1, judges that 1 back the 1st number 2 is prime numbers; Back fork 2 removes 2 multiple, judges that the 1st odd number 3 that is not gone by fork in back of 2 is prime numbers; Back fork 3 removes 3 multiple, judges that the 1st odd number 5 that is not gone by fork in back of 3 is prime numbers; Back fork 5 removes 5 multiple, judges that the 1st odd number 7 that is not gone by fork is prime numbers; Back fork 7 removes 7 multiple, judges that the 1st odd number 11 that is not gone by fork in back of 7 is prime numbers; Carry out like this.
Use fork and go the prime number method of multiplicity to ask the prime number chi, as shown in Figure 5, can directly write out from small to large all prime numbers in the natural number, also can directly write out from small to large and all close number in the natural number.
Fig. 6 is that odd number of the present invention moves poor chi partial schematic diagram.It is rectangular parallelepiped plate shape that odd number moves poor chi, and the above is printed with numeral and graphical information.Go the prime number method of multiplicity to ask mathematics and graphical information on the prime number chi to obtain according to fork.Asking on the prime number chi, remove the even prime number 2 and the quilt that are not gone by fork and pitch all even numbers that go, (comprise the positive odd number 1 that is gone by fork by all remaining odd numbers, the odd number prime number that is not gone by fork and the odd number that is gone by fork close number), by from small to large from left to right horizontally-arranged become delegation, make odd number and move poor chi, printed in the square grid on maximum positive odd number the right one have 3 suspension points " ... " suspension points " ... " a circular aperture has been bored on the right, be convenient to fasten line or the rope that can spur, when installation form or applying template, use.
Fig. 7 is odd number prime number chi partial schematic diagram of the present invention.Odd number prime number chi is rectangular parallelepiped plate shape, and the numeral that the above prints and graphical information go the prime number method of multiplicity to ask numeral and graphical information on the prime number chi to obtain according to fork, or numeral and the graphical information of moving on the poor chi according to odd number obtain.Asking on the prime number chi, remove positive odd number 1, remove even number prime number 2 and remove all and closed number by what fork went, formed a line by erecting from top to bottom from small to large by all remaining odd number prime numbers, be printed on the plate of rectangular shape, odd number prime number 3 tops are printed with the little square grid of 1 blank, be printed in the little square grid of the below of the odd number prime number of following maximum one only have 3 suspension points " ... " again suspension points " ... " the square grid of below has been opened the aperture of a circle, be convenient to fasten line or the rope of pulling, when installation form or applying template, use.
Fig. 8 is the Great Wall line partial schematic diagram on the template cover plate of the present invention.The Great Wall line of " Goldbach's Conjecture proves Great Wall figure " is the character that Great Wall figure shows uniqueness when the Goldbach's Conjecture necessarily sets up, and shows that proof Goldbach's Conjecture ratio is easier to.Space structure shape and the geometric properties thereof of this curve will be not in time, the physical property in place and chemical property change.Usually be printed on the Great Wall line of Goldbach's Conjecture proof on the lower surface of cover plate and on the upper surface of base plate, relatively reverse, overlook from top to bottom and be forward, the Great Wall line of the present invention design also will be at the upper surface of template cover plate along Great Wall line grooving, the metal wire of bright red colored paint that buried japanning, strengthen the three dimensions image of people's vision, increase industrial grade and the scientific and technological content of Great Wall figure template.
The principle of making the Great Wall line is after mobile odd number moves poor chi, below the 1st row even number, since 6, sees from top to bottom, take the 1st odd number prime number as references object, draws the line of a large red below him, then connects into the line that seems the Great Wall and forms.
Fig. 9 is the high ladder line partial schematic diagram on the template cover plate of the present invention.The high ladder line of " Goldbach's Conjecture proves Great Wall figure " is proof Goldbach's Conjecture's an important curve.Geometric properties and the shape of curve never change.Shortcoming is, almost can not show his whole on the figure of Great Wall, has hiding characteristic, shows that the proof Goldbach's Conjecture is very difficult.Usually be printed on the high ladder line of Goldbach's Conjecture proof on the lower surface of cover plate and on the upper surface of base plate, relatively reverse, overlook from top to bottom being forward.The high ladder line of the present invention design also will be at the upper surface of template cover plate along the grooving of high ladder line, and the metal wire of blue lacquer that buried japanning strengthens the three dimensions image of people's vision, increases scientific and technical grade and the scientific and technological content of Great Wall figure template.
Making a day trapezoidal principle is after mobile odd number moves poor chi, on the position of after each odd number moves poor chi translation, determining at last, from odd number prime number 3, below draw the line of a blueness to the right, have on the boundary line, odd prime 3 columns the right to the right next line, if the odd number that institute setting-out top is pitched closes number, just end when moving to the 1st odd number prime number on the alignment of these row.For example, on the figure of Great Wall, it is odd prime 3 that the 24th row and the 46th is listed as in the little square grid that intersects, odd number is moved odd number prime number 3 on the poor chi moves on to the 24th row the 46th row since the 2nd position on the right that is listed as the odd number prime number 89 of the 24th row position to be obtained, below this locational odd number prime number 3, draw blue high ladder line, to just can run into odd number prime number 3 in the small rectangle of the 25th row the 50th row infall through a small rectangle, here, the odd number that the 24th row and the 25th row are all pitched in the 49th row closes number, so just the place, boundary line that moves to the 22nd row and the 23rd row on the high ladder alignment, the below of odd number prime number 19, use at last blue line segment up or down to connect successively each horizontal blue line, form the high ladder line.For this high ladder line, from right-hand, on west by north direction, seem a ladder that leads to Heavenly Palace, prove Great Wall figure high ladder line so be decided to be the Goldbach's Conjecture.
Figure 10 is the neutrality line partial schematic diagram on the template of the present invention.The neutrality line of " Goldbach's Conjecture proves Great Wall figure " is proof Goldbach's Conjecture's an important curve, and the geometrical property perseverance of curve is constant.Use this neutrality line, for people prove the Goldbach's Conjecture, can reduce half to workload, prove M=X+Y, only need be no more than
Figure BDA00002790390800131
Scope in the funtcional relationship Y=M-X of research odd number prime number X and M get final product.Usually the neutrality line on " Goldbach's Conjecture proves Great Wall figure " is printed on the lower surface of cover plate and the upper surface of base plate, relatively reverse, overlook from top to bottom and be forward.The neutrality line of the present invention's design, also will be at the upper surface of template cover plate along the neutrality line grooving, bury the metal wire of golden color lacquer, strengthen the three dimensions image of people's vision, increase " Goldbach's Conjecture proves Great Wall figure " at the scientific and technical content of template inside.
Making the principle of neutrality line, mainly is the positive even numbers M in utilizing template grid the first row, according to formula Y 1+ Y 2Half of=M determined, if Y 1=Y 2, then half of M is odd number prime number Y just, just laterally draws a flavous line segment and indicate in the little square in this odd number prime number of M column Y place.If
Figure BDA00002790390800132
And Then take half of positive integer M as references object, in the M column, see from the bottom up, find greater than
Figure BDA00002790390800134
The odd number prime number in minimum odd number prime number Y 2, find simultaneously less than
Figure BDA00002790390800135
The odd number prime number in maximum odd number prime number Y 1, at Y 1With Y 2A flavous line segment is drawn in the centre position of column, uses at last vertical golden yellow line segment, connects successively from left to right all golden yellow line segments that drawn backward, forms neutrality line of the present invention.
" Goldbach's Conjecture proves Great Wall figure ", since the 3rd row positive even numbers 8 columns, the Great Wall line has the general trend near the 1st row positive even numbers below the 1st row positive even numbers, and indivedual positions are not far from the column positive even numbers.The high ladder line is below the line of Great Wall, and is steeper with respect to the Great Wall line more and more away from the Great Wall line, and neutrality line is on the centre position of Great Wall line and high ladder line, and is with respect to the Great Wall line, milder.
Use respectively Great Wall line, high ladder line and neutrality line in " Goldbach's Conjecture proves Great Wall figure ", each can write the Goldbach's Conjecture's of issuing a certificate a solution, namely 6,8,10,12,14,16,18 ..., all write as two odd number prime numbers and.
Use Great Wall line, high ladder line and neutrality line in " Goldbach's Conjecture proves Great Wall figure ", each can be furtherd investigate from theory orientation, obtains proof line and method with mathematical method Strict Proof Goldbach's Conjecture.
Figure 11 is the oval drawing board synoptic diagram of Goldbach's Conjecture 1+1 of the present invention.Oval drawing board upper surface a kind of color, the above has printed 4 style of writing words, the 1st row is " Goldbach's Conjecture 1+1 ", the 2nd row is " 6=3+3,8=3+5,10=3+7 ", the 3rd row is " 12=5+7; 14=3+11 ", and the 4th row is the suspension points " ... " that six points are arranged, and the illustrated oval drawing board of Figure 11 is installed in figure template lower left, Great Wall.
Figure 12 is the oval drawing board synoptic diagram of Chen Jing profit theorem 1+2 of the present invention.Oval drawing board upper surface a kind of color, upper surface has printed 4 style of writing words, the 1st row is " Chen Jing profit theorem 1+2 ", the 2nd row is " 12=3+3 * 3; 14=5+3 * 3 ", and the 3rd row is " 16=7+3 * 3,18=3+3 * 5 ", the 4th row is suspension points " ... ", and the illustrated oval drawing board of Figure 12 is installed in figure template lower left, Great Wall.
Figure 11 and the oval drawing board of Figure 12 be up and down corresponding arrangements or about side by side arrangement, all look Great Wall figure and grow and wide size, go to determine from the angle of visual appearance.Take up and down corresponding mode of arranging in the file of the present invention.
The illustrated oval drawing board of Figure 11 and Figure 12 can also select other transparent environment-friendly materials to make.
Figure 13 is two Mount Everest drawing boards of Goldbach problem of the present invention synoptic diagram.On this block length side's shape drawing board or transparent poly (methyl methacrylate) plate, the left side is printed on can illustrate a mountain peak of the large theorem of Goldbach, right then be printed on and can illustrate Chen Jing to moisten a mountain peak of large theorem.
On " two Mount Everest drawing boards of Goldbach problem " synoptic diagram, printing two mountain peaks of rising sheer from level ground on the same level face, the mountain peak on the left side is slightly high than the mountain peak on the right.Writing from top to bottom " the large theorem of Goldbach " seven Chinese characters on the mountain peak on the left side, this mountain peak of using the left side represents " the large theorem of Goldbach " relevant with the Goldbach's Conjecture, the formula " 1+1+1+ ...+1+1 " of K 1 addition that is namely connected by (K-1) individual plus sige "+", a series of propositions of the addition formula of K odd number prime number of expression addition, have ... 1+1+1+1+1,1+1+1+1,1+1+1,1+1 is the highest achievement when K is 2, be the Goldbach's Conjecture, simply say into the form of proposition 1+1, the present invention says into " Goldbach's Conjecture 1+1 ", is called as jewel on the number theory imperial crown at international mathematics circle.On this of on the left side mountain peak, seven Chinese characters of " the large theorem of Goldbach " write from top to bottom meaning can be divided two classes: when K is during greater than 2 odd number, for an any such positive odd number K, all are greater than the positive odd number N of 3K, N+2, N+4, N+6, N+8, can be write as K odd number prime number and, when K is during greater than 1 even number, for a so arbitrarily positive even numbers K, all are greater than the positive even numbers M of 3K, M+2, M+4, M+6, M+8, can be write as K odd number prime number and, the correctness of these propositions can be used achievement of the present invention and directly carry out strict mathematical justification.On the mountain peak on the right, from top to bottom, with " the large theorem of Chen Jingrun " six Chinese characters, the meaning be when K be during greater than 1 odd number, for any given such positive integer K, all are greater than the even number 3+3K of 3+3K, (3+3K)+2, (3+3K)+4, (3+3K)+6 ... can be write as and be no more than the long-pending of K odd number prime number, add an odd number prime number and the form of 1+K, here the meaning that " is no more than " refers to can also can not be write to some as the even number of the form of 1+K except writing as the form of 1+K, is write as 1+(K-1 again) form.For example 30=3+3 * 3 * 3 are the form of 1+3, and 32=5+3 * 3 * 3 are the form of 1+3,, 34=7+3 * 3 * 3 are the form of 1+3,36 can not be write as 3 odd number prime numbers long-pending with 1 odd number prime number and form, but can be write as 36=11+5 * 5, be the form of 1+2.Moisten in the large theorem at Chen Jing, the form of 1+3 is not the form of all positive even numbers, because positive even numbers 30,32,34,36,38,40,42 ... in some positive even numbers can not be write as the form of 1+3, can only be write as the form of 1+2, in order to make positive even numbers 30,32,34,36,38,40,42, in all are uninterrupted greater than the positive even numbers of 3+3K, so comprise 1+2, be stated as " for positive odd number 3, all greater than the positive even numbers of 3+3K can be write as be no more than K odd number prime number long-pending add again an odd number prime number and form ".Similarly, the proposition 1+2 of Chen Jingrun proof also is like this.
By Figure 11 of the present invention, Figure 12 and Figure 13, make the reader strictly distinguish Goldbach's Conjecture and the proposition of Chen Jingrun proof.Use " Goldbach's Conjecture proves Great Wall figure ", thereby proved following 3 conclusions: the proposition of (1) Chen Jingrun proof is not the Goldbach's Conjecture; (2) use theory and the method for Chen Jing profit can not prove the Goldbach's Conjecture; (3) achievement that people has been buried Chen Jingrun is that the number theory jewel displays again.
Use the proposition 1+2 that the present invention can prove Chen Jing profit proof, but the conclusion of using Chen Jing profit proof can not prove the Goldbach's Conjecture, thereby show and indirect proof, becoming of Chen Jingrun proof proposition 1+2 is unparalleled in the world, he climbs to the peak of a mathematical problem, has won the number theory jewel of proposition 1+K form.But international mathematics circle is not also recognized this point so far, is the achievement in research that the present invention can directly show yet.
Figure 14 is that Goldbach's Conjecture of the present invention proves Great Wall figure partial schematic diagram." Goldbach's Conjecture proves Great Wall figure " is that the Goldbach's Conjecture proves that Great Wall figure template is installed and use obtains design sketch, can think the planimetric map that each parts of the present invention and all Combination of Methods form.Both can be printed on the environment-friendly materials such as paper, plank, sheet metal, silk are thick, cloth.Be printed on the paper, can be at his upper surface overlay film, anti-oxidation can be mounted cloth at his lower surface again, is protected, and forms the ornament with the good and better appearance of space structure vision.
Can also clamp with the ornament materials of top grade " Goldbach's Conjecture proves Great Wall figure ", in residenter house parlor or study, decorate, roll-shaped " Goldbach's Conjecture proves Great Wall figure " can be put into pupil's school bag, become study integer plus-minus method and popularize Goldbach's Conjecture's maths teaching activities toy, together with Enlightening abacus, help to carry out the learning activities that the student uses one's hands and brains, be can the meet the needs of the world people of various countries' Public Culture product of the present invention.
Figure 15 is that the order of magnitude of the present invention is 2 5Great Wall figure template synoptic diagram.In " Goldbach's Conjecture proves Great Wall figure " template, intercept the part Great Wall figure of from positive even numbers 6 to positive even numbers (26-2), and in the 1st row, remove all positive even numbers 6,8,10,12 ..., 30,32,34 ..., 60,62, can obtain.In the practical application, also can not remove all positive even numbers of the 1st row from 6 to 62, being considered as the order of magnitude during application is 2 5Great Wall figure template on the 1st row positive even numbers conceal.
Figure 16 is that the order of magnitude of the present invention is 2 6Great Wall figure template synoptic diagram.In " Goldbach's Conjecture proves Great Wall figure " template, intercept the part Great Wall figure of from positive even numbers 6 to positive even numbers (27-2), and in the 1st row, remove all positive even numbers 6,8,10,12 ..., 62,64,66 ..., 124,126, can obtain.In the practical application, also can not remove all positive even numbers of the 1st row from 6 to 126, being considered as the order of magnitude during application is 2 6Great Wall figure template on the 1st row positive even numbers conceal.
Figure 17 is that the order of magnitude of the present invention is 2 7Great Wall figure template synoptic diagram.In " Goldbach's Conjecture proves Great Wall figure " template, intercept the part Great Wall figure of from positive even numbers 6 to positive even numbers (28-2), and in the 1st row, remove all positive even numbers 6,8,10,12 ... 62,64,66 ..., 124,126,128,130 ..., 252,254, can obtain.In the practical application, also can not remove all positive even numbers of the 1st row from 6 to 254, being considered as the order of magnitude during application is 2 7Great Wall figure template on the 1st row positive even numbers conceal.
According to the meaning of order of magnitude Great Wall figure template, can regard that the order of magnitude is 2 to Figure 14 " Goldbach's Conjecture proves Great Wall figure " as 10Great Wall figure template.
Figure 18 is that " Goldbach's Conjecture proves Great Wall figure " of the present invention has the solution curve synoptic diagram.In " Goldbach's Conjecture proves Great Wall figure ", press from small to large from left to right order of positive even numbers M, connect the adjacent two odd number prime number Y that list down two row with smooth curve, no matter whether such curve intersects with Great Wall line and neutrality line, and also no matter whether such curve intersects with the high ladder line.Such curve is called Great Wall figure solution curve.Use the solution curve that has on the figure of Great Wall, greater than 4 positive even numbers M, M-Y=X is arranged for arbitrarily, and the be expert at odd number prime number X of the 1st row of certain corresponding the Y of poor X, getting M=X+Y thus is the solution of large even M.
Use Great Wall figure the solution curve synoptic diagram is arranged, if a＞4, for closed zone [a, b] on any one large even M, as M ∈ [a, b] time, have some have solution curve be distributed in large even M column and near, between Great Wall line and neutrality line, have at least one such solution curve to be arranged, between high ladder line and neutrality line, there are some such solution curve to be arranged, for the Great Wall line of positive even numbers M arbitrarily, are positioned at all the time the top of neutrality line, for the high ladder line of any positive even numbers M, be positioned at all the time the below of neutrality line.
If M is the even number greater than 4, in linear function Y=M-X, if odd number prime number that independent variable X is listed as for " Goldbach guess proof Great Wall figure " the upper the 1st, so functional value Y odd number prime number not necessarily.For example, when M=12, if independent variable X=3, then function Y=M-X=12-3=9 is that odd number closes number, and at this moment the form of M=3+3 * 3 is the 1+2 form of Chen Jing profit theorem.
In linear function, if independent variable X is for there being the odd number prime number on the solution curve on " Goldbach is guessed proof Great Wall figure ", independent variable X can also get the Goldbach's Conjecture and prove value on figure Great Wall, Great Wall line, high ladder line, the neutrality line, independent variable X also can get arbitrary odd number prime number of even number M column, so in function Y=M-X, functional value Y must be the odd number prime number, and is the odd number prime number of " Goldbach's Conjecture proves Great Wall figure " upper the 1st row.In research Goldbach's Conjecture's process, people often the former (linear function in the preceding paragraph) as main study subject, thereby very difficult.
Figure 19 is " odd number table of primes " of the present invention synoptic diagram.Odd number prime number in the table is to use the present invention's fork to go the prime number method of multiplicity to ask the prime number chi to obtain.In the table numeral of Latin alphabet N column add numeral that Latin alphabet N is expert at and, be exactly the natural order number of the ascending arrangement of odd number prime number in the table.For example: table look-up 18, get odd number prime number 863 at the 1st row 140 be expert ats and the 1st row 9 column infalls, because 140+9=149, so this odd number prime number 863 is the 149th odd number prime numbers in the ascending ordered series of numbers of lining up of all odd number prime numbers, consider even number prime number 2, can say 2 into is the 0th prime number in the natural order, and the 1st odd number prime number is 3.
Figure 20 is translation number magnitude of the present invention Great Wall figure template synoptic diagram.The present invention here will not state, the direction that can indicate according to arrow among Figure 20 and method are directly used and are got final product, be object of reference with the odd number prime number 3 on the figure template of order of magnitude Great Wall, from left to right, aim at odd number under the 2nd row virgin state and move odd number prime number on the poor chi, carry out a covering, the back is introduced in force.
Figure 21 is that translation odd number of the present invention moves the vertical covering of poor chi with civilian sketch, from 6 to the 40 ascending positive even numbers of arranging from left to right among the 1st row signal Great Wall figure in (1) figure among Figure 21 and (2) chart, odd number moves the virgin state that poor chi does not have translation among the 2nd row signal Great Wall figure, and the odd number that the 1st row odd number prime number 5 is expert among the 3rd row signal Great Wall figure moves the state of poor chi after 1 square net of right translation.The odd number that the 1st row odd number prime number 7 is expert among the 4th row signal Great Wall figure among (2) figure in Figure 21 moves the state of poor chi after 2 square nets of right translation.Shown in (1) figure among Figure 21, in positive even numbers 12 columns, see that from the bottom up the odd number that the 2nd row is gone by fork closes the positive even numbers 12 that has below several 91 odd coefficients 7 to face column the 1st row in the 3rd row, just says to be pitched and go odd number to close several 9 vertically to be covered by odd number prime number 7; The odd number that the 2nd row is gone by fork closes several 15,21,25,33 and is vertically covered by odd number prime number 13,19,23,31 in following the 3rd row respectively.
In Figure 21 (2) figure, namely move during poor chi vertically covers with (2) figure in the civilian sketch at the translation odd number, the 2nd row is closed several 25 and 27 by adjacent two odd numbers that fork goes, and is vertically covered by the odd number prime number 23 of the 3rd row and the 4th row; Adjacent two odd numbers that the 2nd row is gone by fork close several 33 and 35 and are vertically covered by a pair of curved living prime number 29 and 31 of the 4th row.
Translation odd number of the present invention moves the vertical covering of poor chi with civilian sketch among application Figure 21, and be not difficult to find out: odd number moves the odd number that is gone by fork on the poor chi and closes number under virgin state, is moved character and the rule of the vertical covering of poor chi by one or several odd number of translation.
Figure 22 is Great Wall of the present invention figure template synoptic diagram two, the structure of this figure and size are with Great Wall of the present invention figure template synoptic diagram one among Fig. 1 roughly the same, what the form of expression was different is the different synoptic diagram that form in locus that the reader observes, it mainly is the groove that excavates on the indicating template base plate, but even number chi and odd number move in the poor chi insertion groove, back and forth parallel.
A complete work period of the present invention, the cooperatively interact overall process of motion of each member can be divided three classes, and the first kind is 4 members of chi by name, and the even number chi is arranged, and fork goes the prime number method of multiplicity to ask the prime number chi, and odd number moves poor chi, odd number prime number chi.Equations of The Second Kind is 5 methods that the present invention invents, and has fork to remove the prime number method of multiplicity, and odd number moves poor chi and moves method, Great Wall line drawing method, and high ladder line drawing method, the neutrality line technique of painting has 5 methods.
The 3rd class is the experimental technique that the proof Goldbach's Conjecture sets up, and has the translation odd number of the present invention of use to move poor chi method, utilizes the Great Wall collimation method, utilize the high ladder collimation method, utilize the meta collimation method, order of magnitude Great Wall in turn translation method of figure template and both sides folder translation method, utilizing has solution curve method etc.
1, the method for making of partial component of the present invention
Base plate of the present invention, cover plate and in the plate upper surface grooving, the cover plate upper surface is sunken cord, all can directly carry out according to diagramatic content, below the method for making of member of article chi by name.
Example 1 even number chi method for making
On transparent material, laterally print several little squares and be in line, from left to right ascending arrangement positive even numbers 4,6,8,10,12,14,16 ..., 96,98,100 ... guiding ruler edge, the left side, a little square is drawn on last little square middle maximum positive even numbers the right, the right again, the printing suspension points " ... " suspension points " ... " the right bore again an aperture, be convenient to mobile, for use is provided convenience.In addition, can also be for subsequent use from 102 to 200,202 to 300, or 1002 to 1100,1102 to 1200 even number chi, the left side is minimum positive even numbers, the right is maximum positive even numbers, is used for enlarging the scope of positive even numbers.
Example 2 forks go the prime number method of multiplicity to ask prime number chi method for making
Ascending arrangement positive integer 1,2,3 from left to right on the rectangular shape object, 4,5,6,7,8,9,10, fork removes positive odd number 1, judges that 1 back 2 is prime numbers, and the back fork 2 removes 2 multiple, judge that the 1st positive odd number 3 that is not gone by fork in back of 3 must be prime number, back fork 3 removes 3 multiple, and the positive odd number 5 that back the 1st row of judgement 3 is not gone by fork must be prime number, and the back fork 5 removes 5 multiple, judge that the 1st positive odd number 7 that is not gone by fork in back of 5 must be prime number, back fork 7 removes 7 multiple, judges that the 1st positive odd number 11 that is not gone by fork in back of 7 must be prime number,
Use this method, the kindergarten top class in a kindergarten and students in middle and primary schools, all people that can be familiar with number of any age level of various circles of society can both finish this part work, understand this method can be obtained all prime numbers in endless range conclusion.
Example 3 odd numbers move poor chi method for making
Utilize fork to go the prime number method of multiplicity to ask numeral and graphical information above the prime number chi, remove the even number that all are gone and do not gone by fork by fork, remaining odd number, comprise the positive odd number 1 that is gone by fork, do not closed number by the fork all odd number prime numbers that go and all odd numbers that gone by fork and become delegation by from small to large order horizontally-arranged from left to right, be printed on the material of rectangular shape, just made odd number and moved poor chi.Move on the poor chi at odd number, by the odd number pitch close number be blue arabic numeral, little square center, blue digital place has also been drawn one and has been with black to pitch " X ", the odd number prime number that is not gone by fork is the arabic numeral of red coloration.Odd number is moved poor chi insert in " Goldbach's Conjecture proves Great Wall figure " template, under virgin state or after the translation, obtain " Goldbach's Conjecture proves Great Wall figure ", show with black, blueness and red chromatic pattern.
Minimum positive odd number 1 edge, limit that keeps left, maximum positive odd number the right have one be printed on suspension points " ... " square grid, suspension points " ... " the right is drilled with an aperture, is used for pulling strings, and uses when being convenient to move.
Example 4 odd number prime number chi method for makings
Utilize fork to go the prime number method of multiplicity to ask numeral and graphical information above the prime number chi, remove all numbers that gone by fork and the even number prime number 2 that is not gone by fork, by forming a line from top to bottom from small to large, be printed on the transparent environment-friendly materials, the top of minimum odd number prime number 3 is printed on an empty little square grid, the below of maximum odd number prime number be printed on a suspension points " ... " little square grid, suspension points " ... " the below have 1 circular aperture, can overlap line, easy to use.
2. five application of mathematical method of the present invention invention
Most people is popularized international mathematics difficult problem Goldbach's Conjecture in order to meet the needs of the world, so that pupil and people with primary school's schooling can be used for learning mathematics, understand Goldbach's Conjecture's proof, the declarer explains the profound in simple terms, according to the pure mathematics principle, in practice widespread use summarizes the technology of applied mathematics, and following 5 methods are arranged.
Example 5 forks remove the prime number method of multiplicity.
In international mathematics circle and education of middle and primary schools circle, think unanimously that all the distribution of prime number in nature is that milli is random, according to the definition of prime number: in positive integer, if positive integer is except 1 and he itself, do not have other approximate number, so such integer is called prime number.And according to the decision method of prime number: in positive integer, if a positive integer except 1 and he itself, greater than 1 and make divisor less than the positive integer of self, is removed this positive integer with all, the commercial city is not integer, and this positive integer must be prime number so.According to this principle, invention asks the fork of prime number to remove the prime number method of multiplicity.Method is: as long as out arranged sequentially by from small to large of positive integer, become 1,2,3,4,5,6,7,8,9 ... form, the fork remove positive odd number 1, just can judge that 2 must be prime number; Back fork 2 removes all multiples of 2, judges that 2 rear the 1st minimum odd number 3 that is not gone by fork must be a prime number; Back fork 3 removes all multiples of 3, judges that the 1st minimum odd number 5 that is not gone by fork in back of 3 must be a prime number; Back fork 5 removes all multiples of 5, judges that the 1st minimum odd number 7 that is not gone by fork in back of 5 must be a prime number; Back fork 7 removes all multiples of 7, judges that the 1st minimum odd number 11 that does not have fork to go in back of 7 must be a prime number; Like this, forever go on, just obtained all prime numbers in the natural number.
Example 6 odd numbers move poor chi and move method
Four jiaos of the base plate of " Goldbach's Conjecture proves Great Wall figure " template and cover plates are fixed with bolt, the grid of the lower surface of cover plate is overlapped with the grid of end table upper surface, using some odd numbers moves poor chi and inserts in the groove that base plate excavated, all place the left side the 2nd row, the positive odd number 1 that odd number is moved on the poor chi is all aimed at the positive even numbers 4 that the 1st row the 2nd is listed as.The 1st odd number that is positioned at the 2nd row moves poor chi and do not move, and is the original position, is said to be in original state.The odd number prime number and the quilt fork that move on the poor chi from this odd number go odd number to close number, contrast his top the first row positive even numbers, 6,8, and 10,14,16,18,20,22,26,32,34,40,44,46,50 ... below, respectively facing to an odd number prime number, 12,18,24,42, below 48, each row closes number facing to an odd number that is gone by fork, at two continuous positive even numbers 28,30; 36,38; 52,54; 66,68; Below, all face toward one and closed number by the odd number that goes of fork, in other words, uses the virgin state that odd number moves poor chi, the Goldbach's Conjecture can only be to 3 continuous positive even numbers, 6,8,10 establishments.
From the 2nd odd number of the 3rd row moved poor chi, the 1st routine odd number prime number X was object of reference take the left side, calculated the value of X+1, and odd number is moved the from left to right translation of poor chi, and making the positive odd number 1 that is gone by fork on the chi is the positive even numbers of X+1 over against the 1st row intermediate value.For example, in the 3rd row, for the odd number prime number 5 of the 3rd row the 1st row, because 5+1=6, so the odd number of translation the 3rd row moves poor chi, make positive odd number 1 on the chi over against the positive even numbers 6 of the 1st row; In the 4th row, for odd number prime number 7, because 7+1=8, so the odd number of translation the 4th row moves poor chi, make positive odd number 1 on the chi over against the positive even numbers 8 of the 1st row; In the 5th row, for odd number prime number 11, because 11+1=12 so the odd number of translation the 5th row moves poor chi, makes the positive odd number 1 of chi over against the positive even numbers 12 of the 1st row; In the 36th row, for odd number prime number 151, because 151+1=152, so the odd number of translation the 36th row moves poor chi, make positive odd number 1 on the chi over against the positive even numbers 152 of the 1st row; Carry out like this, so infinite.The present invention has omitted each row after the 37th row, and in each the little square grid in the 37th row with suspension points " ... " indicate, illustrate that odd number of the present invention moves poor chi and moves method and can be extended to infinite scope in theory.
Example 7 Goldbach's Conjecture prove the technique of painting of Great Wall line.
The Goldbach's Conjecture who makes as shown in Figure 8 proves the Great Wall line, method for making is: in " Goldbach's Conjecture proves Great Wall figure ", from positive even numbers 6, from left to right ascending, see from top to bottom in each even number column, draw the line segment of a purple on one side of the lower square of the odd number prime number of the 1st redness of not gone by fork, keep straight on up or down again, the limit of the lower square of the odd number prime number of the 1st redness of then not gone by fork second positive even numbers column draws the line segment of a purple, precedence is carried out, and draws the Goldbach's Conjecture and proves the Great Wall line.
Make the concrete grammar of Great Wall line, below positive even numbers 6 columns, a unique odd number prime number 3 in the 2nd row is only arranged, the line segment of just drawing a purple below 3 indicates; Below positive even numbers 8 columns, there are odd prime 5, the 3 row that odd number prime number 3 is arranged at the 2nd row, just below the 1st odd number prime number 5 below the positive even numbers 8, draw the line segment of a purple; Below positive even numbers 10 columns, the 1st odd number prime number is 7, just draws the line segment of a purple below the 1st odd number prime number 7; Below positive even numbers 12, the 1st odd number prime number is 7, just draws the line segment of a purple below odd number prime number 7; Carry out successively.Then from the large red line segment of the odd number prime number 3 of positive even numbers 6 columns, with purple line segment longitudinally, the line segment of the purple that each row has drawn after connecting successively up or down or to the right, obtain at last below the 1st row positive even numbers forming a broken line with the very similar purple of the Great Wall, Goldbach's Conjecture of the present invention exactly proves the Great Wall line.
Example 8 Goldbach's Conjecture prove the technique of painting of high ladder line.
Make Goldbach's Conjecture shown in Figure 9 and prove the high ladder line, method for making is: in " Goldbach's Conjecture proves Great Wall figure ", move position main reference object after the poor chi translation with each row odd number, the standard of the odd number prime number 3 of the minimum of positive even numbers M column below as object of reference, namely from positive even numbers 6 is expert at, from small to large from left to right, the line segment of the blueness of picture of turning right below odd number prime number 3 indicates, to the left side of existing odd number prime number 3 columns of listing of back, end, if institute's setting-out meets by what fork went and closes number, just closing several columns at this sees from the bottom up, find the 1st odd number prime number, the line segment of drawing a blueness below this odd number prime number indicates, connect successively from left to right up or down at last the line segment of the drawn blueness in odd number prime number below with vertically blue line segment behind the sheet, just form Goldbach's Conjecture of the present invention and prove the high ladder line.
Example 9 Goldbach's Conjecture prove the technique of painting of neutrality line.
Make Goldbach's Conjecture shown in Figure 10 and prove neutrality line, method for making is: in " Goldbach's Conjecture proves Great Wall figure ", directly determined by the even number M greater than 4, if
Figure BDA00002790390800212
The 2nd, the odd number prime number is just drawn a flavous line segment that crosses this odd number prime number in the middle of this odd number prime number place square of M column, if
Figure BDA00002790390800211
Not the odd number prime number, just in positive even numbers M column, with
Figure BDA00002790390800221
Be references object, see from the bottom up, find greater than The 1st odd number prime number, again with
Figure BDA00002790390800223
Be references object, see from top to bottom, find less than
Figure BDA00002790390800224
The 1st odd number prime number, on the centre position between these two odd number prime numbers, draw a flavous line segment that crosses this positive even numbers column, connect successively from left to right up or down drawn flavous line segment with golden yellow line segment longitudinally at last backward.
Concrete grammar is for positive even numbers 6, because half of 6 is odd number prime number 3, laterally draws a line segment that crosses 6 columns with regard to square grid centre position, 3 places and indicate; For positive even numbers 8, because half of 8 is 4, and 4 be not the odd number prime number, and take 4 as object of reference, see from the bottom up, 1st the odd number prime number larger than 4 is 5, take 4 as object of reference, see from top to bottom, be 3 than 4 the 1st little odd number prime numbers, afterwards, just laterally drawing a flavous line segment that crosses positive even numbers 8 columns in the centre position of odd number prime number 5 and odd number prime number 3 indicates; For positive even numbers 10, because half of 10 is 5, and 5 are odd number prime numbers, just draw a flavous line segment that crosses positive even numbers 10 columns in 5 places square intermediate lateral and indicate; For positive even numbers 12, because half of 12 is 6, and 6 be not the odd number prime number, take 6 as object of reference, sees from the bottom up, the 1st odd number prime number is 7, take 6 as object of reference, see that from top to bottom the 1st odd number prime number is 5, and 5+7=12 indicates so laterally draw a flavous line segment that crosses positive even numbers 12 columns in 7 and 5 centre position; For positive even numbers 14, because half of 14 is 7, and 7 are odd number prime numbers, and just 7 places square grid centre position is drawn a flavous line segment that crosses 14 columns and indicated; For positive even numbers 16, because half of 16 is 8, and 8 be not the odd number prime number, so 8 be object of reference, sees from the bottom up, the 1st odd number prime number is 13, and take 8 as object of reference, see that from top to bottom the 1st odd number prime number is 3, and 13+3=16 just laterally draws a golden yellow line segment that crosses positive even numbers 16 columns in 13 and 3 centre position; Carry out like this, be expert at since 6 afterwards, downward longitudinally with golden yellow line segment, or upwards connect successively from left to right the golden yellow line segment of each bar that has drawn backward, form at last the Goldbach's Conjecture and prove neutrality line.
3, use the present invention and prove the method that the Goldbach's Conjecture sets up
The present invention mainly invents " Goldbach's Conjecture proves Great Wall figure " template, utilizes the thought of motion, and the natural law of catching template motion overall process to present has been found some natural law, uses these natural laws and innovates, and invention promotes theoretical.The producing principle according to the present invention, increase the technology application function of applied mathematics, three basic method in conjunction with the elementary mathematics representative function: schedule method, imaging method, equation transform, become the method that the pupil can learn and use, middle school student can prove the Goldbach's Conjecture, university student and expert can judge the certain object with space structure of setting up of Goldbach's Conjecture according to " Goldbach's Conjecture proves Great Wall figure ", and be used for illustrating proof procedure and write the conclusion of issuing a certificate, make all use people of the present invention to be sure of that the Goldbach's Conjecture is entirely true.The below introduces the translation odd number and moves poor chi method, utilizes the Great Wall collimation method, utilizes the high ladder collimation method, utilizes the meta collimation method, utilizes order of magnitude Great Wall in turn translation method of figure template and both sides folder translation method, and utilizing has solution curve method etc.
Example 10 translation odd numbers move poor chi method
Move among the embodiment 6 of using method of poor chi at odd number, the odd number of the 2nd row moves poor chi and is fixed, be virgin state, close severally 9 owing to face 1 odd number that is gone by fork below the 1st row positive even numbers 12,3+9=12 is just arranged, this is not the form of Goldbach's Conjecture 1+1, since the 9th, number closed, here, 12=3+3 * 3 are forms of Chen Jing profit theorem 1+2.
Translation odd number of the present invention moves the vertical covering of poor chi with civilian sketch among application Figure 21, and be not difficult to find out: odd number moves the odd number that is gone by fork on the poor chi and closes number under virgin state, is moved character and the rule of the vertical covering of poor chi by one or several odd number of translation.In Figure 21 (1) figure, below closing several 9, the odd number that the 2nd row is gone by fork have 1 odd number prime number 7 to face the positive even numbers 12 of 9 and 7 columns the 1st row in the 3rd row; Below closing several 15, the odd number that the 2nd row is gone by fork have 1 odd number prime number 13 to face the positive even numbers 18 of 15 and 13 columns the 1st row in the 3rd row; Below closing several 21, the odd number that the 2nd row is gone by fork have 1 odd number prime number 19 to face the positive even numbers 24 of 21 and 19 columns the 1st row in the 3rd row; Below closing several 25, the odd number that the 2nd row is gone by fork have 1 odd number prime number 23 to face the positive even numbers 28 of 25 and 23 columns the 1st row in the 3rd row; Below closing several 33, the odd number that the 2nd row is gone by fork have 1 odd number prime number 31 to face the positive even numbers 36 of 33 and 31 columns the 1st row in the 3rd row.Therefore, among (1) figure in Figure 21, the 2nd row odd number moves on the poor chi odd number that is gone by fork and closes several 9,15,21,25,33 and vertically covered by the odd number prime number 7,13,19,23,31 of the 3rd row respectively under virgin state.
In Figure 21 (2) figure, adjacent two odd numbers that the 2nd row is gone by fork close several 25 and 27 and are vertically covered by the odd number prime number 23 of the 3rd row and the 4th row; Adjacent two odd numbers that the 2nd row is gone by fork close several 33 and 35 and are vertically covered by a pair of curved living prime number 29 and 31 of the 4th row.
In Figure 21 (2) figure, namely move during poor chi vertically covers with (2) figure in the civilian sketch at the translation odd number, the 2nd row is closed several 25 and 27 by adjacent two odd numbers that fork goes, and is vertically covered by the odd number prime number 23 of the 3rd row and the 4th row; Adjacent two odd numbers that the 2nd row is gone by fork close several 33 and 35 and are vertically covered by a pair of curved living prime number 29 and 31 of the 4th row.
In " Goldbach's Conjecture proves Great Wall figure ", the odd number prime number X=5 of the 3rd row the 1st row, because 5+1=6, so the odd number of translation the 3rd row moves poor chi, make positive odd number 1 on the chi over against the positive even numbers 6 of the 1st row, be not difficult to find, the odd number of the 3rd row move poor chi from left to right a translation a square grid so that from the 1st, the 2nd, the 3rd row can find out under the positive even numbers place virgin state of the 1st row over against the positive odd number that is gone by fork below 1 odd number prime number has been arranged, make the second interline every 1 even number face the odd number that is gone by fork and close number and remedied by another odd number prime number of the 3rd row or vertically cover so that the Goldbach's Conjecture is in the closed interval [6,26] on, for continuous positive integer 6,8,10,12,14,16,18,20,22,24,26 all set up.Because positive even numbers 28 and 30 columns the 2nd row have been gone two positive odd numbers to close number by fork on the 1st row, but, under virgin state, two odd numbers that gone by fork in interval close several phenomenons under all virgin states, have under the virgin state of the 2nd row and 1 odd number of the 3rd row translation moves poor chi, close number with regard to having become 1 odd number that is gone by fork in interval.All intervals 3,4,5,6,7,8, the individual odd number that is gone by fork closes number, has had the 1st of the 3rd row to be moved poor chi by the odd number after the translation, has just become respectively interval 2,3,4,5,6,7 ... the individual odd number that is gone by fork closes number, and all is to have lacked an odd number that is gone by fork to close several phenomenons.
In " Goldbach's Conjecture proves Great Wall figure ", because the odd number prime number of the 4th row the 1st row infall is 7, and 7+1=8, so the odd number of translation the 4th row moves poor chi, make positive odd number 1 on the chi face the positive even numbers 8 of the 1st row.Be not difficult to find, the odd number of the 4th row move poor chi from left to right a translation two square grids, be equivalent to make under the 2nd row virgin state odd number prime number respectively to two grids of right translation, 2 odd numbers that gone by fork in all intervals close number and are remedied or vertically covered, by the 2nd row, the 3rd row, three odd numbers of the 4th row move the odd number prime number in poor chi translation 5 and the 7 later columns, can find out all positive even numbers 6 on closed interval [6,96], 8,10 ..., 94,96 can both be write as two odd number prime numbers and, the Goldbach's Conjecture is since 6, ends to 96, in the closed interval [6,96] on, all set up for 46 continuous positive even numbers.
Use this translation that odd number moves poor chi, use " Goldbach's Conjecture proves Great Wall figure " template, translation is by 11,13 again, 17,19 four odd numbers that the odd number prime number is expert at move poor chi, have altogether used the 1st row by 3,5,7,11,13,17,19 totally seven determined odd numbers of odd number prime number move poor chi, can obtain the Goldbach's Conjecture on closed interval [6,218], for continuous positive integer 6,8,10,, 216,218 conclusions of all setting up.
Use " Goldbach's Conjecture proves Great Wall figure " can be in odd number prime number value less and in the less scope of odd number number of prime number, carry out odd number is moved the translation of poor chi, obtain the in a big way certain conclusion of setting up of Goldbach's Conjecture.
For example, use by 3,5,7 determine only have 3 odd numbers to move the template of poor chi, the Goldbach's Conjecture is set up in the scope of [6,96] in the closed interval, but we can utilize one section less, just say that the Goldbach's Conjecture necessarily sets up in 26 scopes.
Application is by 3,5, and 7,11,13,17,19 define the template that 7 odd numbers move poor chi, as shown in figure 16, the number of applications level is 26 Great Wall figure template, makes the Goldbach's Conjecture in the closed interval [6,218] certain establishment in the scope, but we can utilize one section less, just say that the Goldbach's Conjecture necessarily sets up in 27 scope.
Application is by 3,5, and 7,11,13,17,19,23 have 8 odd numbers to move the template of poor chi, and as shown in figure 17, the number of applications level is 2 7Great Wall figure template, make the Goldbach's Conjecture in the closed interval certain establishment in the scope of [6,306], we can utilize one section less, just say that the Goldbach's Conjecture is 2 8Scope in certain establishment.
Application has 10 odd numbers to move the template of poor chi, and the number of applications level is 2 8Great Wall figure template, make the Goldbach's Conjecture in the closed interval certain establishment in the scope of [6,554], we can utilize one section less, just say that the Goldbach's Conjecture is 2 9Scope in certain establishment.
Application has 20 odd numbers to move the template of poor chi, and the number of applications level is 2 9Great Wall figure template, make the Goldbach's Conjecture in the closed interval certain establishment in the scope of [6,1024+m], we can utilize one section less, just say that the Goldbach's Conjecture is 2 10Scope in certain establishment.
Be not difficult to find out, only move the template that poor chi is made with less odd number, in " Goldbach's Conjecture proves Great Wall figure " upper translation, can remedy or vertically cover the odd number that is gone by fork and close number, make in larger scope that numerous positive even numbers have solution by becoming without solution, write as two odd number prime numbers and, only there is other positive even numbers not write out, move poor chi but increase the few odd number of number, just solved this problem, Great Wall figure has shown the rule that scope that the Goldbach's Conjecture is set up is doubled and redoubled.
Use this characteristic of " Goldbach's Conjecture proves Great Wall figure " and template, people can directly find out the certain conclusion of setting up of Goldbach's Conjecture.This method of proof, the present invention is called translation template method of verification.Experiment with each subjects such as physics, chemistry, biologies is the same, and this is a method of proof that shows the certain establishment of Goldbach's Conjecture with experiment conclusion.
Example 11 is utilized the Great Wall collimation method
This method shows: in " Goldbach's Conjecture proves Great Wall figure ", the odd number prime number on the line of Great Wall as the 2nd addend Y, and the odd number prime number X of the addend left side that Y is expert at the 1st row as the 1st addend X, get M=X+Y.
Use the Great Wall line in " Goldbach's Conjecture proves Great Wall figure ", can write out successively from small to large the Goethe and guess a solution of establishment with the Bach, and can continuously write in the very large scope and go, its partial solution is as follows:
6=3+3，8=3+5，10=3+7，12=5+7，14=3+11，16=3+13，……，28=5+23，……，98=19+79，……，128=19+109，……，220=23+197，……，310=43+277，……，488=23+457，……，556=47+509，……；854=31+823；……，962=43+919，……，992=73+919，994=3+991，998=7+991，1000=3+997，1002=5+997，……
In order to save space, middle part decomposition is omitted with suspension points " ... ", but these solutions are distributed on the line of Great Wall really.Here, do not affect the effect of the methods and applications " Goldbach's Conjecture proves Great Wall figure " of the present invention's introduction.
Can find out that from the conclusion of utilizing the Great Wall collimation method to obtain in M=X+Y, the value of the 1st addend X all is no more than the value of the 2nd addend Y.
Example 12 is utilized the high ladder collimation method
Use the high ladder line in " Goldbach's Conjecture proves Great Wall figure ", also can write out successively from small to large the solution that the Goldbach's Conjecture sets up.Method be the odd number prime number on the high ladder line as the 1st addend Y, again this odd number prime number be expert at the right the 1st row the odd number prime number as the 2nd addend X, obtain M=Y+X, and can continuously write in the very large scope and go, its partial solution is as follows:
6=3+3，8=3+5，10=3+7，12=5+7，14=3+11，16=3+13，M=Y+X，18=5+13，20=3+17，22=3+19，24=5+19，26=3+23，……
Be not difficult to find out that the conclusion of utilizing the high ladder collimation method to obtain is the same with the conclusion of utilizing the Great Wall line to obtain.But, if the position of two odd number prime number Y and X among the exchange high ladder line addition formula Y+X, the conclusion M=X+Y that obtains, with the conclusion M=X+Y that utilizes the Great Wall line to obtain just be not.
Can find out from " Goldbach's Conjecture proves Great Wall figure ", utilize the Goldbach's Conjecture to prove that the Great Wall line proves that Goldbach's Conjecture's ratio is easier to, usage quantity odd number seldom moves poor chi, just can obtain in very large range positive even numbers can be write as two odd number prime numbers and the conclusion of solution.But, utilize Goldbach's Conjecture's high ladder line proof Goldbach's Conjecture, use many odd numbers and move poor chi, but can only write out seldom several continuous positive even numbers and set up for the Goldbach's Conjecture, the workload that wants to reach the effect of using the Great Wall line is too large.The mathematician is when the research Goldbach's Conjecture both at home and abroad, all climb in this road, so far can't be issued a certificate, it is also more difficult than stepping on the sky to it is believed that, high ladder line from " Goldbach's Conjecture proves Great Wall figure " also can be found out, can't consider wider situation and digital Changing Pattern, the Goldbach's Conjecture of must issuing a certificate is impossible conclusion almost.But use the high ladder line in " Goldbach's Conjecture proves Great Wall figure ", can find out that the Goldbach's Conjecture necessarily sets up from macroscopic view, absolutely not invalid reason.Because above the high ladder line and below the line of Great Wall, also has a lot of solutions, do not used by these two methods, and can find out that from the image of elementary function these two curves are interrupted never, can not be interrupted suddenly yet, for some positive even numbers, suppose that his column does not have the odd number prime number, without separating, so that the Great Wall line of Great Wall figure, high ladder line and neutrality line all have been interrupted, just nothing is separated.But, the positive even numbers of his the right and left, have two odd number prime numbers and equal this positive even numbers, the odd number prime number of left side positive even numbers column is from small to large to grid of right translation so, will remedy or vertically cover the positive even numbers column of being interrupted does not have the state of odd number prime number, the odd number prime number of the positive even numbers column on the right from small to large, all must be obtained by square grid of left side translation, have to through the positive even numbers column of being interrupted, therefore, for positive even numbers column arbitrarily, in " Goldbach's Conjecture proves Great Wall figure ", at least there is 1 odd number prime number Y, so that this positive even numbers column, the difference that M-Y is necessarily arranged is the solution of odd number prime number X, i.e. M-Y=X, get thus M=X+Y, the Goldbach's Conjecture necessarily sets up.
Example 13 is utilized the meta collimation method
In " Goldbach's Conjecture proves Great Wall figure ", utilize neutrality line proof Goldbach's Conjecture, can write out at least a solution.For example, in positive even numbers 6 columns, neutrality line just has 6=3+3 through odd number prime number 3; In positive even numbers 8 columns, neutrality line just has 8=3+5 through between 3 and 5; In positive even numbers 10 columns, neutrality line just has 10=5+5 through odd number prime number 5, also has 10=3+7; In positive even numbers 98 columns, neutrality line closes several 51 through odd number, below neutrality line, 3 odd number prime numbers 37,31 are arranged from big to small, 19, above neutrality line, 3 odd number prime numbers 61,67 are arranged from small to large, 79, so 98=37+61 is arranged, 98=31+67, three solutions of 98=19+79; In positive even numbers 94 columns, neutrality line below neutrality line, also has 4 odd number prime numbers 41,23,11 through odd number prime number 47,5, above neutrality line, also have 4 odd number prime numbers 53,71,83,89, so 5 solution: 94=47+47 are arranged, 94=41+53,94=71+23,94=83+11,94=89+5; Be expert at positive even numbers 128, the neutrality line below has three odd number prime numbers 61,31,19 from big to small, above neutrality line, 3 odd number prime numbers 67,97,109 is arranged, so 3 solutions are arranged, 128=61+67,31+97,19+109;
Use the present invention Great Wall figure as shown in figure 14, from using neutrality line proof Goldbach's Conjecture's solution, use the neutrality line proof Goldbach's Conjecture in " Goldbach's Conjecture proves Great Wall figure " still very difficult.In the scope of closed interval [6,58], prove the Goldbach's Conjecture, utilize the high ladder line among the Great Wall figure that the present invention provides, can only intactly write out all solutions within from 6 to 58 the closed interval [6,58], prove that the Goldbach's Conjecture necessarily sets up.Using neutrality line in the scope of [6,304] in the closed interval, prove the Goldbach's Conjecture, can only completely be all solutions of writing out within from 6 to 304 the closed interval [6,304], proves that the Goldbach's Conjecture necessarily sets up.
Use high ladder line and neutrality line proof Goldbach's Conjecture, obtaining the solution scope more than the Great Wall line in the utilization " Goldbach's Conjecture proves Great Wall figure " has lacked a lot, use the neutrality line in " Goldbach's Conjecture proves Great Wall figure ", in this part work of proof Goldbach's Conjecture, only slightly quite a lot of than the high ladder line of using in " Goldbach's Conjecture proves Great Wall figure ".
Comparative example 11, example 12, example 13, be not difficult to find out, use neutrality line and high ladder line and prove that respectively the Goldbach's Conjecture will be very difficult, ventricumbent direction has spent a lot of time in these phenomenon sides for someone, also do not obtain complete answer, write out the mathematical justification that meets mathematical logic and mathematical programming.
But, use neutrality line, Great Wall line and high ladder line that " Goldbach's Conjecture proves Great Wall figure " shows, be not difficult to find out, neutrality line is always all the time between Great Wall line and high ladder line, along with the positive even numbers span is more and more large, odd number prime number between high ladder line and the Great Wall line is more and more many, is just divided equally by neutrality line.
Think the positive even numbers that does not have solution by mistake for any one people, in " Goldbach's Conjecture proves Great Wall figure ", can not exist, because between Great Wall line and neutrality line, or between neutrality line and high ladder line, also there is a lot of odd number prime numbers, may make never some positive even numbers columns not have the odd number prime number, thereby be interrupted by the Great Wall line, or all in these these row of positive even numbers place, be interrupted by neutrality line, high ladder line and Great Wall line.
In " Goldbach's Conjecture proves Great Wall figure ", for certain several adjacent positive even numbers, suppose that they do not have the odd number prime number at column, and in " Goldbach's Conjecture the proves Great Wall figure " template on their left side, the odd number prime number is arranged, simultaneously, in " Goldbach's Conjecture the proves Great Wall figure " template on the right of this several positive even numbers, the odd number prime number is arranged also, harmlessly establish this and intervally be [c, d], so in the closed interval [6, c-2] on all odd number prime numbers, be attached to odd number and move on the poor chi, from, 3,5,7, beginning, to c-2 end all odd number prime numbers all the square number of squares of translation be 1,2,3,4,5, situation all exist, thereby they must be through each definite even number column of closed interval [c, d], become solution, simultaneously, in the semi-closure half-open interval [d+2 ,+∞) in, the odd number prime number of each even number column is in the closed interval [6, c-2] in the translation process, at first must be through closed interval [c, d], closed interval [c no matter, d] the several positive even numbers in interval, in these several grids, from the 2nd row to by closed interval [3, c-2] definite odd number prime number is through closed interval [c, d] number, can be the several times of the upper positive even numbers number in closed interval [c, d] surely, thereby in " Goldbach's Conjecture proves Great Wall figure ", there is never Goldbach's Conjecture Great Wall line, the phenomenon of neutrality line and day trapezoidal interruption.
Example 14 is made as shown in figure 15, and the order of magnitude of the present invention is 2 5Great Wall figure template
Method is: because 2 5=32, and the minimum odd number prime number greater than 32 is 37, in " Goldbach's Conjecture proves Great Wall figure " template, as long as ascending two the odd number prime numbers 3 of the 1st row and 5 odd numbers of determining move poor chi parallel, just can make closed interval [6,40] become have separate interval, so that the sub-range [6,32] of closed interval [6,40] must be that the interval of solution is arranged, just say that the part Great Wall figure that closed interval [6,40] is determined is that the order of magnitude is 2 5Great Wall figure template, as shown in figure 15.
Because 2 5＜2 6So the order of magnitude is 2 5Great Wall figure template, also can be by closed interval [6,2 6-2] determine that scope makes.
Figure 15 is that the order of magnitude of the present invention is 2 5Great Wall figure template, Figure 24 is " Goldbach's Conjecture proves Great Wall figure " of the present invention, also is that the order of magnitude of the present invention is 2 10Great Wall figure template.
Example 15 is made as shown in figure 16, and the order of magnitude of the present invention is 2 6Great Wall figure template
Method is: because 2 6=64, and the minimum odd number prime number greater than 64 is 67, in " Goldbach's Conjecture proves Great Wall figure " template, as long as ascending two the odd number prime numbers 3 of the 1st row and 5 odd numbers of determining move poor chi parallel, just can make closed interval [6,70] become have separate interval, so that the sub-range [6,64] of closed interval [6,70] must be that the interval of solution is arranged, just say that the part Great Wall figure that closed interval [6,70] is determined is that the order of magnitude is 2 6Great Wall figure template, as shown in figure 16.
Because 2 6＜2 7So the order of magnitude is 2 6Great Wall figure template, also can be by closed interval [6,2 7-2] determine that scope makes.
Example 16 is made as shown in figure 17, and the order of magnitude of the present invention is 2 7Great Wall figure template
Method is: because 2 7=128, and be 131 greater than 128 minimum odd number prime number, in " Goldbach's Conjecture proves Great Wall figure " template, as long as ascending 7 the odd number prime numbers 3,5,7 of the 1st row, 11,13,17,19 odd numbers of determining move poor chi parallel, and closed interval [6,134] is become the interval of solution, so that the sub-range [6,128] of closed interval [6,134] must be that the interval of solution is arranged, just say that the part Great Wall figure that closed interval [6,134] is determined is that the order of magnitude is 2 7Great Wall figure template, as shown in figure 17.
Because 2 7＜2 8So the order of magnitude is 2 7Great Wall figure template, also can be by closed interval [6,2 8-2] determine that scope makes.
In " Goldbach's Conjecture proves Great Wall figure ", because 2 10=1024, and greater than 2 10Minimum odd number prime number be 1031, only need 20 odd number prime numbers 3,5,7,11 of the ascending arrangement of the 1st row, 13,17,19,23,31,37,41,43,47,53,59,61,67,71,73 the odd numbers determined of totally 20 odd number prime numbers move poor chi parallel, closed interval [6,1034] is become the interval of solution, so that closed interval [6,1034] sub-range [6,1024] must be that the interval of solution is arranged, and just says that the part Great Wall figure that closed interval [6,1034] is determined is that the order of magnitude is 2 10Great Wall figure template.
Be 2 at the order of magnitude 6The Great Wall template in, only used number less than 2 2Two less odd number prime numbers 3 and 5, also have number more than 2 3, 15 odd number prime numbers 7,11,13,17,19,23,29,31,37,41,43,47 of from 7 to 61,53,59,61 are distributed in positive even numbers 2 6About column, the interval is [2 3, 2 7] scope in, only used number less than 2 2The odd number prime number, just determined that the order of magnitude is 2 6Great Wall figure template.
Be 2 at the order of magnitude 7The Great Wall template in, only used number less than 2 37 less odd number prime numbers 3,5,7,11,13,17,19, also have number more than 2 4, 23 odd number Prime Number Distribution of from 23 to 127 are 2 at positive even numbers 7About column, the interval is [2 4, 2 8] scope in, only used number less than 2 3The odd number prime number, just determined that the order of magnitude is 2 7Great Wall figure template.
Be 2 at the order of magnitude 10The Great Wall template in, only used number to be less than 2 520 less odd number prime numbers 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73, also have number more than 2 7, 151 odd number Prime Number Distribution of from 79 to 1031 are at positive even numbers 2 10About column, the interval is [2 6, 2 11] scope in, only used number less than 2 520 odd number prime numbers, just determined that the order of magnitude is 2 10Great Wall figure template.
Therefore, use " Goldbach's Conjecture proves Great Wall figure ", directly intercepting is by closed interval [6,2 M+1-2] order of magnitude that scope is determined is 2 mGreat Wall figure template, used in itself less than positive even numbers 2 mAll odd number prime numbers, be 2 with such order of magnitude mGreat Wall figure template, in the closed interval [2 M-1,+∞) carried out the order translation, or the translation of both sides folders, if on the template odd number prime number 3 of the 2nd row and Great Wall figure interval [2m, ∞) the odd number prime number overlap, a lot of length and 2 are just arranged mThe lattice number is 2 M-1Great Wall figure become have separate interval.
In turn translation method of example 17 order of magnitude Great Wall figure templates
As shown in figure 20, in " Goldbach's Conjecture proves Great Wall figure " template, using the Arbitrary Digit magnitude is 2 mGreat Wall figure template, make under the 2nd row virgin state odd number prime number 3 with the closed interval [6 ,+∞) all odd number prime number X 1, X 2, X 3, X 4, X 5... overlap respectively, cover, can find out, many nothings are separated the interval and are separated interval covering, wherein X by having on the template 1＜X 2＜X 3＜X 4＜X 5＜..., so interval [6 ,+∞) in, closed interval [6,2 m], [X 1+ 1, X 1+ 1+2 m], [X 2+ 1, X 2+ 1+2 m], [X 3+ 1, X 3+ 1+2 m], [X 4+ 1, X 4+ 1+2 m], [X 5+ 1, X 5+ 1+2 m] ... all be that the interval of solution is arranged.
For example, the number of applications level is 2 4Great Wall figure template, make under the 2nd row virgin state odd number prime number 3 with the closed interval [6 ,+∞) all odd number prime number X 1, X 2, X 3, X 4, X 5... overlap respectively, cover, can find out, many nothings are separated the interval and are separated interval covering, wherein X by having on the template 1＜X 2＜X 3＜X 4＜X 5＜..., so interval [6 ,+∞) in, closed interval [6,22], [X 1+ 1, X 1+ 1+2 4], [X 2+ 1, X 2+ 1+2 4], [X 3+ 1, X 3+ 1+2 4], [X 4+ 1, X 4+ 1+2 4], [X 5+ 1, X 5+ 1+2 5] ... all be that the interval of solution is arranged.Here, X 1=7, X 2=11, X 3=13, X 4=17, X 5=19 ...
In " Goldbach's Conjecture proves Great Wall figure " template, the number of applications level is 2 7Great Wall figure template, make under the 2nd row virgin state odd number prime number 3 with the closed interval [6 ,+∞) all odd number prime number X 1, X 2, X 3, X 4, X 5... overlap respectively, cover, can find out, many nothings are separated the interval and are separated interval covering, wherein X by having on the template 1＜X 2＜X 3＜X 4＜X 5＜..., so interval [6 ,+∞) in, closed interval [6,134], [X 1+ 1, X 1+ 1+2 7], [X 2+ 1, X 2+ 1+2 7], [X 3+ 1, X 3+ 1+2 7], [X 4+ 1, X 4+ 1+2 7], [X 5+ 1, X 5+ 1+2 7] ... all be that the interval of solution is arranged.
In " Goldbach's Conjecture proves Great Wall figure " template, the number of applications level is 2 10Great Wall figure template, make under the 2nd row virgin state odd number prime number 3 with the closed interval [6 ,+∞) all odd number prime number X 1, X 2, X 3, X 4, X 5... overlap respectively, wherein X 1＜X 2＜X 3＜X 4＜X 5＜..., so interval [6 ,+∞) in, closed interval [6,6+2 10], [X 1+ 1, X 1+ 1+2 10], [X 2+ 1, X 2+ 1+2 10], [X 3+ 1, X 3+ 1+2 10], [X 4+ 1, X 4+ 1+2 10], [X 5+ 1, X 5+ 1+2 10] ... all be that the interval of solution is arranged.
Figure template both sides, example 18 order of magnitude Great Wall folder translation method
Use " Goldbach's Conjecture proves Great Wall figure " template, prove the Goldbach's Conjecture, necessarily have the less template of number of applications level to remove to process the more larger Great Wall figure of the order of magnitude of lattice number in adjacent two determined intervals of odd number prime number.For example, the number of applications level is 2 5Great Wall figure template go to cover by odd number prime number X 1And X 2(X 2-X 1＞2 10) definite closed interval [X 1+ 1, X 2+ 1], just can press from both sides the translation method in figure template both sides, number of applications level Great Wall, as shown in figure 20.
Under " Goldbach's Conjecture proves Great Wall figure " upper the 2nd row virgin state, adjacent two odd number prime number X 1And X 2(X 1＜X 2) lattice of the closed interval determined count the plurality magnitude when larger, the Great Wall figure template that the number of applications level is less proves the Goldbach's Conjecture, just adopts figure template both sides, order of magnitude Great Wall folder translation method.For example, the number of applications level is 2 5Great Wall figure template, remove vertically to cover adjacent two odd number prime number X 1And X 2(X 1＜X 2) definite closed interval [X 1, X 2] and closed interval [X 1, X 2] length be X 2-X 1＞2 10, or X 2-X 1＞2 100, or larger situation, can both obtain closed interval [X 1, X 1+ 2 7] and closed interval [X 2-2 7, X 2] be to have to separate interval proof.
Be 2 at the order of magnitude mGreat Wall figure template in, be 2 according to the order of magnitude mThe definition of Great Wall figure template, the positive even numbers of the 1st row is 4,6,8,10 on the template ..., 2 m-2,2 m, 2 m+ 2 ..., 2 M+1-, maximum odd number prime number is designated as X 2. here Greatly, X GreatlyThan 2 M+1Little, greater than positive even numbers 2 mMinimum odd number prime number be designated as
X Little, so that 2 m＜X Little＜X Greatly＜2 M+1, and closed interval [6, X Little+ 1] be that the solution closed interval is arranged.
The number of applications level is 2 mGreat Wall figure template, at closed interval [X 1, X 2] the left side, with the odd number prime number 3 under the 2nd row virgin state on the template, at the closed interval of Great Wall figure [6, X 1] on from left to right one by one over against or vertically cover all odd number prime numbers under the 2nd row virgin state, demonstrate,prove to get closed interval [X 1, X 1+ 2 m] for the interval of solution is arranged; At closed interval [X 1, X 2] the right, with closed interval [X 1, X 2+ 2 M+1] on positive even numbers M deduct on the template greater than 2 mAll odd number prime number X Little..., X Greatly, calculate M-X, wherein M is closed interval [X 2, X 2+ 2 M+1] on positive even numbers, X is closed interval [X Little, X Greatly] on the odd number prime number, if poor Y is the odd number prime number, i.e. Y=M-X is just with closed interval [X under the 2nd row virgin state on the template Little, X Greatly] upper by linear function Y=M-X(X ∈ [X Little, X Greatly]) all definite odd number prime number X, at the closed interval of Great Wall figure [X 2, X 2+ 2 M+1] on, from right-to-left over against or vertically cover the odd number prime number Y under the 2nd row virgin state among the figure of Great Wall so that with closed interval [X 1, X 2] relevant closed interval [X 1, X 1+ 2 m] and closed interval [X 2-2 m, X 2] and closed interval [X 1, X 2] outer closed interval [X 1-2 m, X 1], [X 2, X 2+ 2 m] etc. become to have and separate intervally, the method for this translation template is called figure template both sides, order of magnitude Great Wall folder translation method.
The implementation method of operating is easy, only has for two steps.For example, the below is take the order of magnitude as 2 7The Great Wall artwork be example, illustrate that both sides folders moves the application of method, proves closed interval [2 in the figure of Great Wall 9, 2 10] must be that the interval of solution is arranged, can carry out as follows:
In the 1st step, to right translation: on " Goldbach's Conjecture proves among the figure of Great Wall ", the translation number magnitude is 2 from left to right 7Great Wall figure template.Because less than 2 7The odd number prime number have 3,5,7,, 113,127, one has 30, this can directly obtain from Figure 19 of the present invention " odd number table of primes " synoptic diagram, the odd number prime number 3 of the 2nd row on the template successively over against or vertically cover closed interval among the figure of Great Wall [6,900] and determine all odd number prime numbers under the 2nd row virgin state, can obtain making closed interval [512,1024] by without separating interval becoming the conclusion of separating the interval being arranged, can also obtain closed interval [1024,1024+2 7] must be to have to separate interval conclusion.
In the 2nd step, to left: on " Goldbach's Conjecture proves Great Wall figure ", the translation number magnitude is 2 from right to left 7Great Wall figure template.Because the order of magnitude is 2 7Great Wall figure template on closed interval [6,134] must be to have to separate intervally, and closed interval [128,256] have 25 odd number prime numbers 131,137 of arranging from small to large, 139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251, these 25 odd number prime numbers are all than 2 7Greatly, and all than 2 8Little, wherein, minimum odd number prime number is X Little=131, maximum odd number prime number is X Greatly=251, these 25 odd number prime numbers on the figure template of Great Wall are all used, enough prove closed interval [2 9, 2 10] must be that the interval of solution is arranged.Here, in the 2nd step, the present invention only uses maximum this odd number prime number X Greatly=251, just can obtain the conclusion that needs, make closed interval [2 9, 2 10] be that the interval of solution is arranged, because the positive even numbers of Great Wall figure on closed interval [882,1282] from big to small, has 1282,1272,1270,1264,1260,1248,1242,1234,1228,1222,1218,1204,1198,1192,1188,1180,1170,1162,1158,1138,1134,1132,1128,1114,1110,1108,1104,1090,1080,1078,1074,1072,1062,1060,1048,1038,1024,1020,1012,1008,1002,994,990,984,978,970,960,952,942,938,932,924,912,910,904,898,894,892,882, these even numbers, one has 59, respectively deducts 251, and its difference all is the odd number prime number, and corresponding one by one, respectively 1031,1021,1019,1013,1009,997,991,983,977,971,967,953,947,941,937,929,919,911,907,887,883,881,877,863,859,857,853,839,829,827,823,821,811,809,797,787,773,769,761,757,751,743,739,733,727,719,709,701,691,683,677,673,661,659,653,647,643,641,631, so the number of applications level is 2 7Great Wall figure template, the odd number prime number 251 of the 2nd row on this template from right-to-left over against or vertically cover on the figure of Great Wall under the 2nd row virgin state tactic odd number prime number 1031,1021,1019,1013,1009,997 by from big to small, 991,983,977,971,967,953,947,941,937,929,919,911,907,887,883,881,877,863,859,857,853,839,829,827,823,821,811,809,797,787,773,769,761,757,751,743,739,733,727,719,709,701,691,683,677,673,661,659,653,647,643,641,631, just obtained closed interval [2 9, 2 10] by without separating interval becoming the conclusion of separating the interval being arranged.
In fact, be 2 at the order of magnitude 7Great Wall figure template on, less than 2 7Odd number prime number one have 53, still, on closed interval [6,30000], the difference of two odd number prime numbers that all are adjacent is all less than 2 7, that is to say that the little foursquare lattice number at interval is all less than 50 under the 2nd row virgin state in the figure of Great Wall between adjacent two odd number prime numbers, the usage quantity level is 2 7Great Wall figure template, not only can prove closed interval [2 9, 2 10] for the interval of solution is arranged, can also prove that closed interval [1000,30000] is that the interval of solution is arranged.Using both sides folder translation method and the order of magnitude is 2 7Great Wall figure template, can also Great Wall figure upper left close right open interval [30000 ,+∞) upper many without separating interval [X, X+2 7] all become to have and separate interval [X, X+2 7].
In the both sides of Figure 20 folder translation partial schematic diagram, the number of applications level is 2 5Great Wall figure template, carry out over against or vertically cover, prove that " Goldbach's Conjecture proves Great Wall figure " middle order of magnitude is 2 7Closed interval [2 6, 2 7] separate intervally for having, from positive even numbers 6 to positive even numbers 128, namely the closed interval [6,2 7] upper all positive even numbers M can be write as two odd number prime numbers and X+Y.
On " Goldbach's Conjecture proves Great Wall figure ", intercepting is from positive even numbers 4 to 2 6A part of Great Wall figure of-2, can make the order of magnitude is 2 5Great Wall figure template.
The usage quantity level is 2 5Great Wall figure template, use both sides folder translation method, finish first the 1st step, from left to right parallel.Be the order of magnitude 2 5Great Wall figure template under the 2nd row virgin state odd number prime number 3 over against or vertically cover all odd number prime numbers 3,5,7,11,13 under " Goldbach's Conjecture proves Great Wall figure " upper the 2nd row virgin state ..., 29,31, X 1, X 2, X 3..., X n..., except closed interval [6,32] and closed interval [32,62] all are all closed intervals [29+3,29+3+2 are arranged outside the interval of solution 5], [31+3,31+3+2 5], [X 1+ 3, X 1+ 3+2 5], [X 2+ 3, X 2+ 3+25] ..., [X n+ 3, X n+ 3+2 5] ... all be that the interval of solution is arranged, because there are 14 odd number prime numbers to be respectively on closed interval [60,130]: 61,67,71,73,79,83,89,87,89,97,101,103,107,109,113,127, and 61+3=64,64+2 5=96, so be 2 with the order of magnitude 5Great Wall figure template, over against or vertically cover, make odd number prime number 3 cover 64, all positive even numbers columns of 64 to 96 on the figure of Great Wall have the odd number prime number so, all being capped without separating the interval under Great Wall figure the 2nd row virgin state.In like manner, because 89+3=92,97+3=100, and 92+32=124,100+32=132 is so be 2 with the order of magnitude 5Great Wall figure template, over against or forward cover, make odd number prime number 3 cover respectively 89 and 97, so, on the figure of Great Wall from 92 to 124, all positive even numbers columns of from 100 to 132, the odd number prime number is arranged, and all being capped without separating the interval on the figure of Great Wall under the 2nd row virgin state is so that closed interval [64,128] for the interval of solution is arranged, this has just proved that with the order of magnitude be 2 5Great Wall figure template proved closed interval [2 on the figure of Great Wall 6, 2 7] separate interval conclusion for having.
Finished for the 2nd step, parallel is 2 at the order of magnitude from right to left again 5Great Wall figure template on because have 5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 in the scope of closed interval [6,62], altogether 16 odd number prime numbers will be 2 with the order of magnitude 5Great Wall figure template proof closed interval [2 6, 2 7] for the interval of solution is arranged, calculating the poor of M-X, M is the positive even numbers on the closed interval [60,130], because 130-59=71,130-47=83,130-41=89,130-29=101,130-23=107,130-17=113,130-3=127 is so from the right-to-left parallel, be 2 with the order of magnitude 5Great Wall figure template on odd number prime number 59,47,41,29,23,17,3, respectively over against or vertically cover positive even numbers 130 on the figure of Great Wall, just can be by 130-59=71,130-47=83,130-41=89,130-29=101,130-23=107,130-17=113,130-3=127, just can prove that closed interval [74,130] is for there being the interval of solution.In like manner because 76-53=23, so the positive even numbers 76 that covers on the figure of Great Wall with odd number prime number 53, just can prove closed interval [24,76] for have separate interval, thereby obtain closed interval [24,130] for the solution interval is arranged.At this moment, need not to use shown in the both sides folder partial schematic diagram of Figure 20, cover 110,43 with 47 again and cover 104,41 cover 102,, 29 cover 96,23 covers 84,19 cover 78,, 11 coverings 64 etc., but can guarantee to prove that conclusion is reliable from more safe direction. this has just proved that with the order of magnitude be 2 5Great Wall figure template proof Great Wall figure on closed interval [2 6, 2 7] separate interval conclusion for having.
Use both sides folder translation method, both the translation number magnitude was 2m(from left to right mPositive integer, and m 〉=3) Great Wall figure template, prove closed interval [2 M+1, 2 M+2] for the interval of solution is arranged, can right-to-left translation number magnitude be 2 again mThe Great Wall figure template of (m is positive integer, and m 〉=3) proves closed interval [2 M+1, 2 M+2] separate intervally for having, this is because the order of magnitude is that 2m(m is positive integer, and m 〉=3) Great Wall figure template on [6,2 M+1-2] for have separate interval, and by Qi Beixiaofu---Bei Telunde theorem " if x＞1 has an odd number prime number at least on [x, 2x] then in the closed interval ", know closed interval [2 M+1, 2 M+2] on have an odd number prime number at least, this is the ultimate principle that both sides folders translation method can prove the Goldbach's Conjecture.
Conclusion: in " Goldbach's Conjecture proves Great Wall figure ", the number of applications level is 2 mGreat Wall figure template, if make on the template odd number prime number 3 under the 2nd row virgin state over against or vertically cover the upper left right open interval [2 that closes of Great Wall figure mAll odd number prime number X of ,+∞) 1, X 2, X 3, X 4..., X I-1, X i, X I+1..., infinite a plurality of closed interval [X must be arranged 1, X 1+ 2 m], closed interval [X 2, X 2+ 2 m], closed interval [X 3, X 3+ 2 m], closed interval [X 4, X 4+ 2 m] ..., closed interval [X I-1, X I-1+ 2 m], closed interval [X i, X i+ 2 m], closed interval [X I+1, X I+1+ 2 m] ... all for the interval of solution is arranged.Wherein, X 1＜X 2＜X 3＜X 4＜...＜X I-1＜X i＜X I+1＜...If X i-X I-1≤ 2 m, so, the number of applications level is 2 mGreat Wall figure template, closed interval [X on the apparent easily proof Great Wall figure I-1, X i] for the interval of solution is arranged; If X i-X I-1＞2 m, so, one proves closed interval [X surely I-1-2 m, X I-1], closed interval [X I-1, X I-1+ 2 m], closed interval [X i-2 m, X i], closed interval [X i, X i+ 2 m] all be that the interval of solution is arranged.
Use the result that above the 1st step and the 2nd step obtain, be not difficult to know, work as X 2-X 1＞2 mThe time, closed interval [X 1+ 3, X 2+ 3] there is the lattice number of solution to increase at least on Individual, closed interval [X 1+ 3, X 2+ 3] upper lattice number without separating has reduced [(2 at least m+ X Little)-2] individual.
This phenomenon that figure template both sides, Great Wall folder translation method produces, the natural law of the Great Wall line in " Goldbach's Conjecture proves Great Wall figure " exactly: in the odd number prime number of the 1st row, the less odd number prime number from small to large of usage quantity, the interval that solution just can much be arranged in a big way, and make the Great Wall line successive, more and more near the 1st row even number and away from neutrality line.In the odd number prime number of the 1st row, if the more odd number prime number from small to large of usage quantity, the number of solution that just can obtain each positive even numbers in a big way is more.
Having and separate interval and without separating interval length on " Goldbach's Conjecture proves Great Wall figure " template, is exactly to separate interval and without separating interval size, represents with the lattice number in interval.The 1st odd numbers of being determined by odd number prime number 3 are moved poor chi insert the 2nd row in " Goldbach's Conjecture proves Great Wall figure " template, make positive odd number on the chi over against the positive even numbers 4 of the 1st row, so, at adjacent two odd number prime number X 1And X 2Between, closed interval [X 1, X 2] length be X 2-X 1, under original state, his is (X without separating the interval 1, X 2), have and separate the interval (X that is 1-2, X 1+ 2) with (X-2, X 2+ 2), there are the lattice of separating the interval to count U=2, without separating interval lattice number W = X 2 - X 1 2 - 1 , Interval [X 1, X 2] the lattice number G = U + W = X 2 - X 1 2 + 1 .
For example, at adjacent two odd number prime number X 1=23, X 2On=29 closed intervals [23,29] of determining, separate interval (21,25) and (27,31) interior positive even numbers and have the lattice of solution to count U=2 having, i.e. odd number prime number 23 and 29 liang of lattice without the lattice number in solution interval are
Figure BDA00002790390800344
I.e. 25 and 27 liang of lattice, so the lattice on closed interval [23,29] are counted G=4, namely 23,25,27,29.Corresponding with it, because M 1=X 1+ 3, M 2=X 2+ 3, at closed interval [M 1, M 2] on, there are the interval lattice of solution to count U=2, i.e. M 1=23+3=26, M 2=29+3=32 is without separating interval lattice number Or W = M 2 - M 1 2 - 1 , I.e. 28 and 30 liang of lattice.
At closed interval [M 1, M 2] and [X 1, X 2] on, if M 1=X 1+ 3, and M 2=X 2+ 3, lattice number in these two intervals so, these two have that to separate interval lattice numbers and these two of equal value respectively without separating interval lattice numbers, and U=2, namely W = X 2 - X 1 2 - 1 , Or W = M 2 - M 1 2 - 1 , G＝U+W。
Use odd number prime number X 1And X 2Closed interval [the X that determines 1, X 2] the positive even numbers M corresponding with application 1And M 2Determine closed interval [M 1, M 2], discuss usefulness " Goldbach's Conjecture proves Great Wall figure " and prove that Goldbach's Conjecture's effect has equivalence.
Example 19 " Goldbach's Conjecture proves Great Wall figure " has solution curve, as shown in figure 18.
Figure 18 is that the present invention has the solution curve synoptic diagram.Optional two positive even numbers a, b(a＜b), in the closed interval [a, b], can do some has solution curve.
In " Goldbach's Conjecture proves Great Wall figure ", for any one positive even numbers, as long as his column has solution curve, below this positive even numbers, no matter pile up vertical setting of types so what closed number by the odd numbers that go of fork, this positive even numbers M can be by there being the odd number prime number Y on the solution curve to add the with it odd number prime number X of correspondence of right-hand member that solution curve is expert at the 1st row, obtain M=Y+X, i.e. the result of X+Y=M.
In " Goldbach's Conjecture proves Great Wall figure ", when positive even numbers M 〉=6, below any one positive even numbers M, can find out: when M is larger, except Goldbach's Conjecture Great Wall line, high ladder line, neutrality line, also have some to have solution curve to cross M-2, M, three determined closed intervals of positive even numbers of M+2 [M-2, M+2] surpass 3 solution so that positive even numbers M necessarily has, each solution be two odd number prime numbers and, and these several solutions are all identical never.
Great Wall line in " Goldbach's Conjecture proves Great Wall figure " has shown the natural law that the Goldbach's Conjecture sets up naturally, moves poor chi at the application odd number and moves in the method, and following 5 important principles are arranged, and guarantees that the Goldbach's Conjecture necessarily sets up.
1. mobile any odd number moves poor chi, makes in the 2nd row the 1st odd number move poor chi and is in static virgin state, utilizes " Goldbach's Conjecture proves Great Wall figure ", also can obtain infinite a plurality of make large even M can be write as two odd number prime number X and Y's and form, wherein, X=3, M=X+Y.
2. use the odd number prime number and move poor chi, 1 addition formula of every calculating X+1, for example calculate 5+1=6, can obtain from " Goldbach's Conjecture proves Great Wall figure " infinite a plurality of provable Goldbach's Conjecture's addition formula, even number M write as two odd number prime number X and Y's and form M=X+Y.
3. in " Goldbach's Conjecture proves Great Wall figure ", shown three line principles: Great Wall line, high ladder line and neutrality line infinitely extend, and never be interrupted, the Great Wall line always is positioned at the trend that there is close the 1st row even number the neutrality line top, the high ladder line always below neutrality line, has the trend away from Great Wall line and neutrality line.Except Great Wall line, neutrality line and high ladder line, also naturally demonstrate between them many odd number prime numbers by up and down between two row about form thickly dotted Great Wall figure between two row solution curve arranged, people can be found out from large even M corresponding to these curves can be write out more than 3 and different solution, each solution is two odd number prime number X and Y's and X+Y, obtains the result of M=X+Y.
4. use " Goldbach's Conjecture proves Great Wall figure " and prove the Goldbach's Conjecture, under cover two wires unification principle: the phenomenon of high ladder line and line two wires, Great Wall unification principle, translation number magnitude template, be equivalent at the Great Wall mobile, the place that template arrives, corresponding the high ladder line of column, but who does not see, as being submerged in the Mariana Trench, the Pacific Ocean of bottomless chasm, enhanced very difficultly, and who can not go to promote.Very easy to right translation by the 1st row the 1st row, upwards promoted by the capable N row of N, unusually difficult, prove very much difficulty of Goldbach's Conjecture, be equivalent to people and go to the deep-sea to seek the equally reason of difficulty of high ladder line.Usage quantity level template of the present invention translation has been equivalent to use the easy computing of mathematics, changes and embarrasses easily.
5. the number of applications level is 2 mGreat Wall figure template can prove that the order of magnitude is 2 M+1, 2 M+2" Goldbach's Conjecture proves Great Wall figure " in the Great Wall line necessarily exist.Order of magnitude of every usefulness is 2 mGreat Wall figure template, the scope that the proof Goldbach's Conjecture sets up in the figure of Great Wall will be doubled, or quadruples, can also obtain the order of magnitude is 2 M+1The Great Wall template, can go round and begin again loops.
Use above 4 character, the additive theory of numbers principle in conjunction with using Hua Luogeng can also prove the Goldbach's Conjecture in the other direction by additive method.

Claims (2)

1. the Goldbach's Conjecture proves Great Wall artwork board manufacturing method, it is characterized in that: prove that by the Goldbach's Conjecture template cover plate (1), template plate (2), even number chi (3), odd number prime number chi (4), the odd number of Great Wall figure move some of poor chis (5), Great Wall line (6), neutrality line (7), high ladder line (8), the oval drawing board (9) of Goldbach's Conjecture 1+1, the oval drawing board (10) of Chen Jing profit theorem 1+2 and two Mount Everest drawing boards of Goldbach problem (11) and consist of;
Described Goldbach's Conjecture refers to can be write as two odd number prime number X and Y's and X+Y greater than 4 even number M;
Described prime number refer to if positive integer except 1 and he itself, do not have other approximate number, this positive integer is prime number so, minimum prime number is 2, is unique even number prime number, all the other all prime numbers all are odd numbers, are the odd number prime numbers greater than 2 prime number namely;
Described template cover plate (1) lower surface and template plate (2) upper surface are printed on title and the little square net that the Goldbach's Conjecture proves Great Wall figure, relatively reverse, overlook in the same way, specification is identical, template cover plate (1) lower surface reverse printed, the printing of template plate (2) upper surface forward, template cover plate (1) upper surface is inlaid with Great Wall line (6), neutrality line (7) and high ladder line (8); On template plate (2), every delegation form is equipped with groove, is used for inserting odd number and moves poor chi (5) or even number chi (3);
Described even number chi (3) upper surface has printed 4,6,8,10,12 ... a row positive even numbers, can in template plate (2), move in the 1st row groove the 2nd row the position;
Described odd number prime number chi (4) upper surface has printed 3,5,7,11,13,17,19,23 ... a row odd number prime number;
Described odd number moves poor chi (5) and forms according to ask numeral and the graphic making on the prime number chi that fork goes the prime number method of multiplicity to make, use odd number and move the top data of poor chi (5), remove by fork go close the number and 1, made odd number and moved poor chi (5), odd number moves poor chi (5) upper surface and has printed
Figure FDA00002790390700011
A row positive odd number, there have the positive odd number that gone by fork and odd number to close to be several 9,15,21 etc., and the odd number prime number 3,5,7,11,13,17,19 etc. that is not gone by fork is also arranged;
(2) four jiaos of described template cover plate (1), template plates are equipped with pilot hole;
The method for making of described Great Wall line (6), prove among the figure of Great Wall the Goldbach's Conjecture, from positive even numbers 6, from left to right ascending, see from top to bottom in each even number column, a line segment is drawn on one side in the lower square of the 1st the odd number prime number that is not gone by fork, keep straight on up or down again, a line segment is drawn on the limit of the lower square of the 1st the odd number prime number that is not then gone by fork second positive even numbers column, carry out successively, draw the Goldbach's Conjecture and prove the Great Wall line, be Great Wall line (6);
The method for making of described neutrality line (7) proves among the figure of Great Wall the Goldbach's Conjecture, directly determined by the even number M greater than 4 in the 1st row, if
Figure FDA00002790390700021
Be the odd number prime number, just in the middle of this odd number prime number place square of M column, draw a line segment that crosses this odd number prime number, if
Figure FDA00002790390700022
Not the odd number prime number, just in positive even numbers M column, with
Figure FDA00002790390700023
Be references object, for all greater than
Figure FDA00002790390700024
Odd number, see from the bottom up, find the 1st odd number prime number, again with
Figure FDA00002790390700025
Be references object, to all less than
Figure FDA00002790390700026
Odd number, see from top to bottom, find the 1st odd number prime number, on the centre position between these two odd number prime numbers, draw a line segment that crosses this positive even numbers column, connect successively from left to right up or down drawn line segment with this line segment longitudinally at last backward, be neutrality line (7);
The method for making of described high ladder line (8), prove among the figure of Great Wall the Goldbach's Conjecture, the position is as the main reference object after moving poor chi translation take each row odd number, the standard of the odd number prime number 3 of the minimum of positive even numbers M column below as object of reference, namely from positive even numbers 6 is expert at, from small to large from left to right, the line segment of picture of turning right below odd number prime number 3 indicates, to the left side of existing odd number prime number 3 columns of listing of back, end, if institute's setting-out meets by what fork went and closes number, just closing several columns at this sees from the bottom up, find the 1st odd number prime number, below this odd number prime number, draw a line segment and indicate, connect successively from left to right up or down drawn line segment below the odd number prime number with this line segment longitudinally at last backward, be high ladder line (8);
The oval drawing board (9) of described Goldbach's Conjecture 1+1 is elliptical flat-plate, is printed on the four lines literal on it, the first behavior " Goldbach's Conjecture 1+1 ", the 2nd behavior " 6=3+3,8=3+5,10=3+7 ", the 3rd behavior " 12=5+7,14=3+11 ", the 4th behavior suspension points " ... ";
The oval drawing board (10) of described Chen Jing profit theorem 1+2 is elliptical flat-plate, is printed on the four lines literal on it, the 1st behavior " Chen Jing profit theorem 1+2 ", the 2nd behavior " 12=3+3 * 3,14=5+3 * 3 ", the 3rd behavior " 16=7+3 * 3,18=3+3 * 5 ", the 4th behavior suspension points " ... ";
Two Mount Everest drawing boards of described Goldbach problem (11) are the rectangular parallelepiped transparent panel, and this plate upper left side is printed on can illustrate the synoptic diagram on the large theorem of Goldbach mountain peak, and the right side is printed on can illustrate Chen Jing to moisten the synoptic diagram on large theorem 1+2 mountain peak.
2. the Goldbach's Conjecture proves Great Wall figure template using method, it is characterized in that: prove among the figure of Great Wall the Goldbach's Conjecture, requirement according to the proof Goldbach's Conjecture, positive even numbers M is write as the form of X+Y, grid on the 1st row at the square blank grid of 3 tops on the odd number prime number chi and positive even numbers M-2 place is overlapped, in the M column, see from top to bottom, each odd number prime number can be used as Y, a left side is seen on the odd number prime number chi with Y at the odd number prime number X with delegation, just can be write as the form of M=X+Y, one is used for proving the effective addition formula of Goldbach's Conjecture exactly, or the result who directly reads X+Y=M.
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